复化梯形公式,辛普森公式的matlab程序
matlab复化Simpson求积公式计算数值积分
,(k 0,1,...,n)k x a kh =+=b a h n-=2221222121(x)dx (x)dx [(x )4(x )(x )]3k k m a x b x k m k k k k f f h f f f -=--=≈≈++∑⎰⎰∑复化Simpson 求积公式计算数值积分一·复化Simpson 求积公式的数学理论如果用分段二次插值函数近似被积函数，即在小区间上用Simpson 公式计算积分近似值，就可导出复化Simpson 公式。
二·复化Simpson 求积公式的算法和流程图将积分区间[a,b]分成n=2m 等分，分点为,在每个小区间[222,x k k x -]（k=0,1,…,n-1）上。
用Simpson 公式求积分，则有2222222221222212(x)dx [(x )4(x )(x )]6[(x )4(x )(x )]3kk x k k k k k x k k k x x f f f f h f f f -------≈++=++⎰求和得整理后得到122111(x)dx [(a)(b)2(x )4(x )]3m m bk k a k k h f f f f f --==≈+++∑∑⎰ （5-21）式（5-21）称为复化Simpson 公式。
如果(4)(x)[a,b]f c ∈，则由Simpson 插值余项公式可得复化公式的截断误差为1221115(4)2221()(x)dx [(a)(b)2(x )4(x )]3(2h)()[x ,x ]2880m m bS k k a k k mk k k h R f f f f f f ξξ--==-==-+++=-∈∑∑⎰∑因为(4)f x 为连续，故存在[a,b]ξ∈，使得(4)(4)11()()m k k f f m ξξ==∑代入上式得5(4)4(4)1(2h)()()()(a,b)2880180m s k b a R f mf h f ξξξ=-=-=-∈∑ （5-22）式（5-22）表明，步长h 越小，截断误差越小。
复合梯形公式、复合辛普森公式matlab
复合梯形公式、复合⾟普森公式matlab 1. ⽤1阶⾄4阶Newton-Cotes公式计算积分程序：function I = NewtonCotes(f,a,b,type)%syms t;t=findsym(sym(f));I=0;switch typecase 1,I=((b-a)/2)*(subs(sym(f),t,a)+subs(sym(f),t,b));case 2,I=((b-a)/6)*(subs(sym(f),t,a)+4*subs(sym(f),t,(a+b)/2)+...subs(sym(f),t,b));case 3,I=((b-a)/8)*(subs(sym(f),t,a)+3*subs(sym(f),t,(2*a+b)/3)+...3*subs(sym(f),t,(a+2*b)/3)+subs(sym(f),t,b));case 4,I=((b-a)/90)*(7*subs(sym(f),t,a)+...32*subs(sym(f),t,(3*a+b)/4)+...12*subs(sym(f),t,(a+b)/2)+...32*subs(sym(f),t,(a+3*b)/4)+7*subs(sym(f),t,b));case 5,I=((b-a)/288)*(19*subs(sym(f),t,a)+...75*subs(sym(f),t,(4*a+b)/5)+...50*subs(sym(f),t,(3*a+2*b)/5)+...50*subs(sym(f),t,(2*a+3*b)/5)+...75*subs(sym(f),t,(a+4*b)/5)+19*subs(sym(f),t,b));case 6,I=((b-a)/840)*(41*subs(sym(f),t,a)+...216*subs(sym(f),t,(5*a+b)/6)+...27*subs(sym(f),t,(2*a+b)/3)+...272*subs(sym(f),t,(a+b)/2)+...27*subs(sym(f),t,(a+2*b)/3)+...216*subs(sym(f),t,(a+5*b)/6)+...41*subs(sym(f),t,b));case 7,I=((b-a)/17280)*(751*subs(sym(f),t,a)+...3577*subs(sym(f),t,(6*a+b)/7)+...1323*subs(sym(f),t,(5*a+2*b)/7)+...2989*subs(sym(f),t,(3*a+4*b)/7)+...1323*subs(sym(f),t,(2*a+5*b)/7)+...3577*subs(sym(f),t,(a+6*b)/7)+751*subs(sym(f),t,b));endsyms xf=exp(-x).*sin(x);a=0;b=2*pi;I = NewtonCotes(f,a,b,1)N=1:I =N=2:I =N=3:I =(pi*((3*3^(1/2)*exp(-(2*pi)/3))/2 - (3*3^(1/2)*exp(-(4*pi)/3))/2))/4N=4:I =(pi*(32*exp(-pi/2) - 32*exp(-(3*pi)/2)))/452. 已知，因此可以通过数值积分计算的近似值。
MATLAB数值分析实验二(复合梯形、辛普森和龙贝格求积,以及二重积分计算等)
佛山科学技术学院实 验 报 告课程名称 数值分析 实验项目 数值积分专业班级 机械工程 姓 名 余红杰 学 号 2111505010 指导教师 陈剑 成 绩 日 期 月 日一、实验目的1、理解如何在计算机上使用数值方法计算定积分⎰badxx f )(的近似值;2、学会复合梯形、复合Simpson 和龙贝格求积分公式的编程与应用。
3、探索二重积分⎰⎰Ddxdy y x f ),(在矩形区域},|),{(d y c b x a y x D ≤≤≤≤=的数值积分方法。
二、实验要求（1） 按照题目要求完成实验内容； （2） 写出相应的Matlab 程序；（3） 给出实验结果(可以用表格展示实验结果)； （4） 分析和讨论实验结果并提出可能的优化实验。
（5） 写出实验报告。
三、实验步骤1、用不同数值方法计算积分149xdx =-（1）取不同的步长h ，分别用复合梯形及复合辛普森求积计算积分，给出误差中关于h 的函数，并与积分精确值比较两公式的精度。
（2）用龙贝格求积计算完成问题（1）。
2、给出一种求矩形区域上二重积分的复化求积方法，然后计算二重积分xyDedxdy -⎰⎰，其中积分区域{01,01}D x y =≤≤≤≤。
1.%Int_t.m 复化梯形：function F = Int_t(x1,x2,n)% 复化梯形求积公式% x1,x2 为积分起点和中点%分为n个区间，没选用步长可以防止区间数为非整数。
%样点矩阵及其函数值：x = linspace(x1,x2,n+1);y = f(x);m = length(x);%本题中用Matlab计算端点位置函数值为NaN,故化为零：y(1) = 0;y(m) = 0;%算出区间长度，步长h：h = (x2 -x1)/n;a = [1 2*ones(1,m-2) 1];%计算估计的积分值：F = h/2*sum(a.*y);%f.mfunction y = f(x)y = sqrt(x).*log(x);%run11.mclc,clear;%分为10个区间，步长0.1的积分值：F = Int_t(0,1,10);F10 = F%分为100个区间F = Int_t(0,1,100);F100 = F%误差计算W10 = abs((-4/9)-F10);W100 = abs((-4/9)-F100);W = [W10 W100]%复化辛普森：%Int_s.mfunction F = Int_s(x1,x2,n)% 复化梯形求积公式% x1,x2 区间，分为n个区间。
matlab软件求解数值积分及复化梯形公式、复化公式估计误差的方法心得
MATLAB软件是数值计算和科学计算的强大工具，尤其在数值积分和数值微积分中，它提供了许多内置函数，可以快速有效地解决各种问题。
以下是我使用MATLAB求解数值积分，以及使用复化梯形公式和复化公式估计误差的一些心得：1. 数值积分：MATLAB的内置函数`integral`可以用于数值积分。
这个函数使用自适应Simpson方法，可以处理复杂函数的积分。
我发现，对于一些非标准函数，`integral`函数能够给出相当精确的结果。
2. 复化梯形公式：复化梯形公式是一种数值积分的方法，它通过把积分区间分成许多小的子区间，然后在每个子区间上应用梯形法则来近似积分。
在MATLAB中，我们可以使用梯形法则的公式来实现这个方法。
值得注意的是，为了得到更精确的结果，我们需要将子区间的数量增加。
3. 复化公式估计误差：估计复化梯形公式的误差是重要的，因为它可以帮助我们了解我们的近似有多准确。
误差可以通过比较复化梯形公式的近似值和真实值来估计。
在MATLAB中，我们可以使用try-catch语句来捕获可能的错误，并据此调整我们的近似。
4. 细心和耐心：在使用MATLAB进行数值计算时，细心和耐心是关键。
我们需要仔细检查我们的代码，确保所有的变量都被正确地定义和使用。
同时，由于数值计算可能会产生一些意想不到的结果，我们需要有耐心去调试和优化我们的代码。
5. 理解你的算法：对于任何数值方法，理解其背后的数学原理是非常重要的。
这不仅可以帮助你理解你的代码是如何工作的，而且当出现问题时，你可以更有效地找到问题的根源。
6. 使用MATLAB的文档和社区：MATLAB的文档非常全面，对于不熟悉某个函数或方法的人来说，查阅文档是非常有帮助的。
此外，MATLAB的社区也非常活跃，当你遇到问题时，你可以在这里寻求帮助。
以上就是我在使用MATLAB求解数值积分以及使用复化梯形公式和复化公式估计误差的一些心得。
总的来说，MATLAB是一个功能强大的工具，但是要充分利用它，我们需要理解其背后的数学原理，耐心地调试我们的代码，并善于利用其文档和社区资源。
复化梯形公式和复化辛普生公式
（英文版）Two regulations promulgated for implementation is in the party in power for a long time and the rule of law conditions, the implementation of comprehensive strictly strategic plan, implementation in accordance with the rules and discipline to manage the party, strengthen inner-party supervision of major initiatives. The two regulations supporting each other, the < code > adhere to a positive advocate, focusing on morality is of Party members and Party leading cadres can see, enough to get a high standard; < rule > around the party discipline, disciplinary ruler requirements, listed as "negative list, focusing on vertical gauge, draw the party organizations and Party members do not touch the" bottom line ". Here, the main from four square face two party rules of interpretation: the first part introduces two party Revised regulations the necessity and the revision process; the second part is the interpretation of the two fundamental principles of the revision of laws and regulations in the party; the third part introduces two party regulations modified the main changes and needs to grasp several key problems; the fourth part on how to grasp the implementation of the two regulations of the party. < code > and < Regulations > revised the necessity and revised history of the CPC Central Committee the amendment to the Chinese CommunistParty members and leading cadres honest politics several guidelines > and < Chinese Communist Party discipline and Punishment Regulations > column 1 by 2015 to strengthen party laws and regulations focus. Two party regulations revision work lasted a Years, pooling the wisdom of the whole party, ideological consensus, draw historical experience, respect for the wisdom of our predecessors, which reflects the unity of inheritance and innovation; follow the correct direction, grasp the limited goals, adhere to the party's leadership, to solve the masses of the people reflect a focus on the problem. The new revision of the < code > and < rule >, reflects the party's 18 and the eighth session of the third, the spirit of the fourth plenary session, reflecting the experience of studying and implementing the General Secretary Xi Jinping series of important speech, reflects the party's eighteen years comprehensive strictly practice. (a) revised two regulations of the party need of < the ICAC guidelines > in < in 1997 Leaders as members of the Communist Party of China clean politics certain criteria (Trial) > based on revised, the promulgation and implementation of January 2010, to strengthen the construction of the contingent of leading cadres play an important role. But with the party to manage the party strictly administering the deepening, has not been able to fully meet the actual needs. Content is toocomplicated, "eight prohibition, 52 are not allowed to" hard to remember, and also difficult to put into practice; the second is concisely positive advocated by the lack of prohibited provisions excessive, no autonomy requirements; the third is banned terms and discipline law, both with the party discipline, disciplinary regulations repeat and Criminal law and other laws and regulations repeat; the fourth is to "clean" the theme is not prominent, not for the existing problems, and is narrow, only needle of county-level leading cadres above. < rule > is in 1997 < Chinese Communist Party disciplinary cases (Trial) > based on revision, in December 2003 the promulgation and implementation, to strengthen the construction of the party play very important role. Along with the development of the situation, which many provisions have been unable to fully meet the comprehensive strictly administering the practice needs. One is Ji law, more than half of the provisions and criminal law and other countries laws and regulations Repetition; two is the political discipline regulations is not prominent, not specific, for violation of the party constitution, damage the authority of Party Constitution of misconduct lack necessary and serious responsibility to pursue; third is the main discipline for the leading cadres, does not cover all Party members. Based on the above situation, need to < the criterion of a clean and honestadministration > and < rule > the two is likely to be more relevant regulations first amendment. By revising, really put the authority of Party discipline, the seriousness in the party tree and call up the majority of Party members and cadres of the party constitution of party compasses party consciousness. (II) two party regulations revision process the Central Committee of the Communist Party of China attaches great importance to two regulations revision . Xi Jinping, general books recorded in the Fifth Plenary Session of the eighth session of the Central Commission for Discipline Inspection, on the revised regulations < > made clear instructions. According to the central deployment, the Central Commission for Discipline Inspection from 2014 under six months begin study two regulations revision. The Standing Committee of the Central Commission for Discipline Inspection 4 review revised. Comrade Wang Qishan 14 times held a special meeting to study two regulations revision, amendment clarifies the direction, major issues of principle, path and target, respectively held a forum will listen to part of the province (area) secretary of the Party committee, Secretary of the Discipline Inspection Commission, part of the central ministries and state organs DepartmentThe first party committee is mainly responsible for people, views of experts and scholars and grassroots party organizations andParty members. Approved by the Central Committee of the Communist Party of China, on 7 September 2015, the general office of the Central Committee of the Party issued a notice to solicit the provinces (autonomous regions, municipalities) Party, the central ministries and commissions, state ministries and commissions of the Party (party), the General Political Department of the military, every 3 people organization of Party of two regulations revision opinion. Central Commission for Discipline Inspection of extensive solicitation of opinions, careful study, attracting, formed a revised sent reviewers. In October 8 and October 12, Central Committee Political Bureau Standing Committee and the Political Bureau of the Central Committee After consideration of the two regulations revised draft. On October 18, the Central Committee of the Communist Party of China formally issued two regulations. Can say, two laws amendment concentrated the wisdom of the whole party, embodies the party. Second, < code > and < Regulations > revision of the basic principles of two party regulations revision work and implement the party's eighteen, ten eight plenary, the spirit of the Fourth Plenary Session of the Eleventh Central Committee and General Secretary Xi Jinping important instructions on the revised < low political criterion > and < Regulations >, highlighting the ruling partycharacteristics, serious discipline, the discipline quite in front of the law, based on the current, a long-term, advance as a whole, with Bu Xiuding independent < rule > and < rule >. Main principle is: first, adhere to the party constitution to follow. The constitution about discipline and self-discipline required specific, awaken the party constitution of party compasses party consciousness, maintaining the authority of the constitution. General Secretary Xi Jinping pointed out that "no rules, no side round. Party constitution is the fundamental law, the party must follow the general rules. In early 2015 held the eighth session of the Central Commission for Discipline Inspection Fifth Plenary Session of the 16th Central Committee, Xi Jinping again pointed out that constitution is the party must follow the general rules, but also the general rules." the revision of the < code > and < rule > is Method in adhere to the regulations established for the purpose of combining rule of virtue is to adhere to the party constitution as a fundamental to follow, the constitution authority set up, wake up the party constitution and party rules the sense of discipline, the party constitution about discipline and self-discipline specific requirements. 4 second is to adhere to in accordance with the regulations governing the party and the party. The Party of rule of virtue "de", mainly refers to the party's ideals and beliefs, excellent traditional style. The revised the< code > closely linked to the "self-discipline", insisting on the positive initiative, for all members, highlight the "vital few", emphasized self-discipline, focusing on the morality, and the majority of Party members and the ideological and moral standards. The revised < > Ji method separately, Ji, Ji Yan to Method, as a "negative list", emphasizing the heteronomy, focusing on vertical gauge. Is this one high and one low, a positive reaction, the strict party discipline and practice results transformation for the integration of the whole party to observe moral and discipline requirements, for the majority of Party members and cadres provides benchmarking and ruler. Third, insist on to. In view of the problems existing in the party at the present stage, the main problems of Party members and cadres in the aspect of self-discipline and abide by the discipline to make clearly defined, especially the party's eighteen years strict political discipline and political rules, organization and discipline and to implement the central eight provisions of the spirit against the four winds and other requirements into Disciplinary provisions. Not one pace reachs the designated position, focusing on in line with reality, pragmatic and effective. After the revision of major changes, major changes in the < code > and < rule > modified and needs to grasp several key problems (a) < code > < code > adhere to according to regulationsgoverning the party and party with morals in combination, for at the present stage, the leadership of the party members and cadres and Party members in existing main problems of self-discipline, put forward principles, requirements and specifications, showing Communists noble moral pursuit, reflected at all times and in all over the world ethics from high from low 5 common requirements. One is closely linked to the "self-discipline", removal and no direct relation to the provisions of . the second is adhere to a positive advocate, "eight prohibition" 52 are not allowed to "about the content of the" negative list moved into synchronization amendment < cases >. Three is for all the party members, will apply object from the leadership of the party members and cadres to expand to all Party members, fully embodies the comprehensive strictly required. The fourth is prominent key minority, seize the leadership of the party members and cadres is the key, and put forward higher requirements than the ordinary Party members. Five is to simplify, and strive to achieve concise, easy to understand, easy to remember. The revised < code > is the ruling Party since the first insists on a positive advocate forAll Party members and the self-discipline norms, moral declaration issued to all members of the party and the National People's solemn commitment. > < criterion of a clean and honest administration consists of 4 parts, 18,more than 3600 words. After the revision of the < code >, a total of eight, 281 words, including lead, specification and Party member cadre clean fingered self-discipline norms, etc. Part 3 members low-cost clean and self-discipline, the main contents can be summarized as "four must" "eight code". Lead part, reiterated on ideal and faith, fundamental purpose, the fine traditions and work style, noble sentiments, such as "four must" the principle of requirements, strong tone of self-discipline, The higher request for 6 and supervised tenet, the foothold in permanent Bao the party's advanced nature and purity, to reflect the revised standards requirements. Members of self-discipline norms around the party members how to correctly treat and deal with the "public and private", "cheap and rot" thrifty and extravagance "bitter music", put forward the "four norms". Party leader cadre clean fingered self-discipline norms for the leadership of the party members and cadres of the "vital few", around the "clean politics", from civil servant of the color, the exercise of power, moral integrity, a good family tradition and other aspects of the leadership of the party members and cadres of the "four norms" < > < norm norm. "The Party member's self-discipline norms" and "party members and leading cadre clean fingered self-discipline norms," a total of eight, collectively referred to as the "eight". "Four must" and "eight" of thecontent from the party constitution and Party's several generation of leaders, especially Xi Jinping, general secretary of the important discussion, refer to the "three discipline and eight points for attention" statements, and reference some embody the Chinese nation excellent traditional culture essence of epigrams. (2) the revised regulations, the main changes in the revised Regulations > to fully adapt to the strictly requirements, reflects the according to the regulations governing the law of recognition of deepening, the realization of the discipline construction and Jin Ju. < rule > is party a ruler, members of the basic line and follow. And the majority of Party members and cadres of Party organizations at all levels should adhere to the bottom line of thinking, fear discipline, hold the bottom line, as a preventive measure, to keep the party's advanced nature and purity. 1, respect for the constitution, refinement and discipline. Revised < rule > from comprehensive comb physical constitution began, the party constitution and other regulations of the Party of Party organizations and Party discipline requirements refinement, clearly defined in violation of the party constitution will be in accordance with regulations to give the corresponding disciplinary action. The original 10 categories of misconduct, integration specification for political discipline, discipline, honesty and discipline masses Ji Law and discipline and discipline andother six categories, the content of < rule > real return to Party discipline, for the majority of Party members and listed a "negative list. 7 2, highlighting the political discipline and political rules. > < Regulations according to the stage of the discipline of outstanding performance, emphasizing political discipline and political rules, organization and discipline, in opposition to the party's leadership and the party's basic theory, basic line, basic program and basic experience, the basic requirement of behavior made prescribed punishment, increase the cliques, against the organization such as violation of the provisions, to ensure that the central government decrees and the Party of centralized and unified. 3, adhere to strict discipline in the law and discipline In front, Ji separated. Revised < Regulations > adhere to the problem oriented, do Ji separated. Any national law existing content, will not repeat the provisions, the total removal of 79 and criminal law, repeat the content of the public security management punishment law, and other laws and regulations. In the general reiterated that party organizations and Party members must conscientiously accept the party's discipline, die van comply with national laws and regulations; at the same time, to investigate violations of Party members and even criminal behavior of Party discipline and responsibility, > < Regulations distinguish five different conditions, with special provisions weremade provisions, so as to realize the connection of Party discipline and state law. 4, reflect Wind building and anti-corruption struggle of the latest achievements. < rule > the party's eighteen years implement the spirit of the central provisions of the eight, against the requirements of the "four winds" and transformation for disciplinary provisions, reflecting the style construction is always on the road, not a gust of wind. In the fight against corruption out of new problems, increase the trading rights, the use of authority relatives profit and other disciplinary terms. Prominent discipline of the masses, the new against the interests of the masses and ignore the demands of the masses and other disciplinary terms and make provisions of the disposition and the destruction of the party's close ties with the masses.Discipline to protect the party's purpose. 8 of these regulations, a total of three series, Chapter 15, 178, more than 24000 words, after the revision of the regulations a total of 3 series, Chapter 11, 133, 17000 words, divided into "general" and "special provisions" and "Supplementary Provisions" Part 3. Among them, add, delete, modify the provisions of the proportion of up to nearly 90%. 1, the general general is divided into five chapters. The first chapter to the regulations of the guiding ideology, principles and scope of application of the provisions, highlight the strengthening of the partyconstitution consciousness, maintenance the authority of Party Constitution, increase the party organizations and Party members must abide by the party constitution, Yan Centralized centralized, would examine at all levels of the amended provisions implementing and maintaining Party discipline, and consciously accept the party discipline, exemplary compliance with national laws and regulations. The second chapter of discipline concept, disciplinary action types and effects of the regulations, will be a serious warning from the original a year for a year and a half; increase the Party Congress representative, by leaving the party above (including leave probation) punishment, the party organization should be terminated its representative qualification provisions. The third chapter of the disciplinary rules of use prescribed in the discipline rectifying process, non convergence, not close hand classified as severely or heavier punishment. "Discipline straighten "At least eighteen years of five years, these five years is to pay close attention to the provisions of the central eight implementation and anti -" four winds ". The fourth chapter on suspicion of illegal party disciplinary distinguish five different conditions, with special provisions were made provisions, to achieve effective convergence of Party and country 9 method. < rule > the provisions of Article 27, Party organizations in thedisciplinary review found that party members have committed embezzlement, bribery, dereliction of duty dereliction of duty and other criminal law act is suspected of committing a crime shall give cancel party posts, probation or expelled from the party. The second is < Regulations > Article 28 the provisions of Party organizations in the disciplinary review But found that party members are stipulated in the criminal law, although not involved in a crime shall be investigated for Party discipline and responsibility should be depending on the specific circumstances shall be given a warning until expelled punishment. This situation and a difference is that the former regulation behavior has been suspected of a crime, the feeling is quite strict, and the latter for the behavior not involving crime, only the objective performance of the provisions of the criminal code of behavior, but the plot is a crime to slightly. < Regulations > the 29 provisions, Party organizations in the discipline review found that party members and other illegal behavior, affect the party's image, the damage to the party, the state and the people's interests, we should depend on the situation Seriousness given disciplinary action. The loss of Party members, seriously damaging the party's image of behavior, should be given expelled from the party. At this article is party member is in violation of the criminal law outside the other illegal acts, such as violatesthe public security administration punishment law, customs law, financial laws and regulations behavior. The fourth is < cases > Article 32 stipulates, minor party members and the circumstances of the crime, the people's Procuratorate shall make a decision not to initiate a prosecution, or the people's court shall make a conviction and exempted from criminal punishment shall be given within the party is removed from his post, probation or expelled from the party. Party members and crime, sheets were fined in accordance with For acts; the principal Ordinance amended the provisions of the preceding paragraph. This is the new content, in order to achieve Ji method effective convergence. Five is < > the thirty third article 10 of the provisions, the Party member due to an intentional crime is sentenced to criminal law (including probation) sheets or additional deprivation of political rights; due to negligence crime and was sentenced to three years or more (excluding three years) a penalty, shall give expelled punishment. Due to negligence crime is convicted and sentenced to three years (including three years) in prison or be sentenced to public surveillance, detention, shall in general be expelled from the party. For the individual may not be expelled from the party, should control Approval. This is followed and retained the original > < Regulations the provisions of punishment party authorization rules and report to a level partyorganizations. For is "party members with criminal acts, and by the criminal punishment, generally should be expelled from the party". The fifth chapter of probationary Party member of the discipline and discipline after missing members of the treatment and punishment decisions, such as the implementation of the provisions, clear the related party discipline and punishment decision made after, for duties, wages and other relevant alteration formalities for the longest time. 2, sub sub section will the original regulations of10 categories of acts of violation of discipline integration revised into 6 categories, respectively, in violation of the punishments for acts of political discipline "in violation of discipline behavior of punishment" in violation of integrity of disciplinary action points "of violation punishments for acts of mass discipline" "the violation of work discipline, punishment" in violation of discipline of life behavior punishment "6 chapters. 3, annex" Supplementary Provisions "clear authority making supplementary provisions of, cases of interpretative organ, as well as regulations implementation time and retroactivity etc.. 11 (3) learning understanding > < regulations needs to grasp several key problems The first problem -- about the violation of political discipline behavior > < new ordinance chapter 6 the political discipline column for the six disciplines, that is the main opposition to Party leadership and the opposition of the basictheory, basic line, basic program and basic experience, basic requirements of misconduct made provisions of the disposition, especially the eighteen since the CPC Central Committee put forward the Yan Mingzheng treatment of discipline and political rules requirements and practical achievements transformation for Discipline article, increase the false debate central policies, cliques, against the organization review, make no discipline of the principle of harmony terms. These are the party's eighteen years in comprehensive strictly Process combined with the practice of rich content. (1) false debate the central policies and undermine the Party of centralized and unified the problem is made in accordance with the provisions of the party constitution. Constitution in general programme requirements adhere to democratic centralism is one of the requirements of the construction of the party must adhere to the four cardinal. Application of this principle is not only the party the basic organization principle and is also the mass line in party life, it requires that we must fully develop inner-party democracy, respect for the dominant position of Party members, safeguarding the Party member democratic rights, give full play to the enthusiasm and creativity of the party organizations at all levels and Party members, at the same time, also must implement the right concentration, ensure the party's mission < the chaos in unity and concertedaction to ensure that the party's decision to get quickly and effectively implementing. The Party Central Committee formulated the major principles and policies, through different channels and ways, fully listen to the party organizations and Party members of the opinions and suggestions, but 12 is some people face to face not to say back blather "" will not say, after the meeting said, "" Taiwan does not say, and nonsense ", in fact, not only disrupt the people thought, some causing serious consequences, the damage to the Party of the centralized and unified, hinder the central policy implementation, but also a serious violation of the democratic system of principles. There is no doubt that shall, in accordance with the Regulations > 4 Specified in Article 6 to give the appropriate punishment. For did not cause serious consequences, to give criticism and education or the corresponding tissue processing. (2) about the destruction of the party's unity < New Regulations > the forty eighth to fifty second article, to damage Party's unity unified and violation of political discipline, punishment situation made explicit provisions. Article 52 of the new "in the party get round group, gangs seek private gain, cliques, cultivate private forces or through the exchange of interests, for their own to create momentum and other activities to gain political capital, given a serious warning or withdraw from their party posts disposition; if thecircumstances are serious, to give Leave a party to observation or expelled from the party. (3) on against the organization review of the provisions of the constitution, party loyalty honesty is party members must comply with the obligations. Members must obey the organization decision, shall not violate the organization decided encounters by asking questions to find organization, rely on the organization, shall not deceive the organization, against the organization. For example, after the investigation does not take the initiative to explain the situation, but to engage in offensive and defensive alliance, hiding the stolen money is against survey organization, is a violation of the behavior of political discipline. Article 24 of the original > < Regulations, although the provisions of the interference, hinder group review the behavior of the fabric can be severely or 13 Aggravated punishment, but did not put this kind of behavior alone as a discipline for qualitative amount of discipline. > < new regulations increase the Article 57, "anti organization review, one of the following acts, given a warning or serious warning; if the circumstances are relatively serious, giving removed from or placed on probation within the party post; if the circumstances are serious, give expelled from the party: (a) on supply or forged, destroyed, transfer, conceal evidence; (II) to prevent others expose, providing evidence。
复化梯形公式和复化Simpson公式
数值计算方法上机题目3一、计算定积分的近似值：221x e xe dx =⎰ 要求：（1）若用复化梯形公式和复化Simpson 公式计算，要求误差限71021-⨯=ε，分别利用他们的余项估计对每种算法做出步长的事前估计；（2）分别利用复化梯形公式和复化Simpson 公式计算定积分；（3）将计算结果与精确解比较，并比较两种算法的计算量。
1.复化梯形公式程序：程序1（求f （x ）的n 阶导数：syms xf=x*exp(x) %定义函数f （x ）n=input('输入所求导数阶数:')f2=diff(f,x,n) %求f(x)的n 阶导数结果1输入n=2f2 =2*exp(x) + x*exp(x)程序2：clcclearsyms x%定义自变量xf=inline('x*exp(x)','x') %定义函数f(x)=x*exp(x)，换函数时只需换该函数表达式即可f2=inline('(2*exp(x) + x*exp(x))','x') %定义f(x)的二阶导数,输入程序1里求出的f2即可。
f3='-(2*exp(x) + x*exp(x))'%因fminbnd（）函数求的是表达式的最小值，且要求表达式带引号，故取负号，以便求最大值e=5*10^(-8) %精度要求值a=1 %积分下限b=2 %积分上限x1=fminbnd(f3,1,2) %求负的二阶导数的最小值点，也就是求二阶导数的最大值点对应的x值for n=2:1000000 %求等分数nRn=-(b-a)/12*((b-a)/n)^2*f2(x1) %计算余项if abs(Rn)<e %用余项进行判断break% 符合要求时结束endendh=(b-a)/n %求hTn1=0for k=1:n-1 %求连加和xk=a+k*hTn1=Tn1+f(xk)endTn=h/2*((f(a)+2*Tn1+f(b)))z=exp(2)R=Tn-z %求已知值与计算值的差fprintf('用复化梯形算法计算的结果 Tn=')disp(Tn)fprintf('等分数 n=')disp(n) %输出等分数fprintf('已知值与计算值的误差 R=')disp(R)输出结果显示：用复化梯形算法计算的结果 Tn= 7.3891等分数 n=7019已知值与计算值的误差 R= 2.8300e-0082. Simpson公式程序：程序1：（求f（x）的n阶导数）：syms xf=x*exp(x) %定义函数f（x）n=input('输入所求导数阶数:')f2=diff(f,x,n) %求f(x)的n阶导数结果1输入n=4f2 =4*exp(x) + x*exp(x)程序2：clcclearsyms x%定义自变量xf=inline('x*exp(x)','x') %定义函数f(x)=x*exp(x)，换函数时只需换该函数表达式即可f2=inline('(4*exp(x) + x*exp(x))','x') %定义f(x)的四阶导数，输入程序1里求出的f2即可f3='-(4*exp(x) + x*exp(x))'%因fminbnd（）函数求的是表达式的最小值，且要求表达式带引号，故取负号，一边求最大值e=5*10^(-8) %精度要求值a=1 %积分下限b=2 %积分上限x1=fminbnd(f3,1,2) %求负的四阶导数的最小值点，也就是求四阶导数的最大值点对应的x值for n=2:1000000 %求等分数nRn=-(b-a)/180*((b-a)/(2*n))^4*f2(x1) %计算余项if abs(Rn)<e %用余项进行判断break% 符合要求时结束endendh=(b-a)/n %求hSn1=0Sn2=0for k=0:n-1 %求两组连加和xk=a+k*hxk1=xk+h/2Sn1=Sn1+f(xk1)Sn2=Sn2+f(xk)endSn=h/6*(f(a)+4*Sn1+2*(Sn2-f(a))+f(b)) %因Sn2多加了k=0时的值，故减去f(a)z=exp(2)R=Sn-z %求已知值与计算值的差fprintf('用Simpson公式计算的结果 Sn=')disp(Sn)fprintf('等分数 n=')disp(n)fprintf('已知值与计算值的误差 R=')disp(R)输出结果显示：用Simpson公式计算的结果 Sn= 7.3891等分数 n=24已知值与计算值的误差 R= 2.7284e-008用复化梯形公式计算的结果为：7.3891，与精确解的误差为：2.8300e-008。
数值分析数值微积分实验
实验报告
一、实验目的
复化求积公式计算定积分。
二、实验题目
1.用复化梯形公式、复化辛普森公式求下列定积分，要求绝对误差为3
10-=ε，并将计算结果与精确解进行比较： dx e x e x 232
143
2⎰= 三、实验原理
复化求积公式程序，复化辛普森公式程序。
四、实验内容及结果
五、实验结果分析
实验1中复化梯形公式和复化辛普森公式的比较：
运行复化梯形公式的时候，因为要去找区分精度，所以花的时间比较长，需要将区间分为365份时才能达到规定的误差范围。
而复化辛普森公式则只需要将区间分为12份即可。
说明复化辛普森比较好。
复化梯形公式matlab
复化梯形公式matlab在MATLAB中，可以使用复化梯形公式来进行数值积分的计算。
复化梯形公式是将积分区间分割成多个小区间，在每个小区间上采用梯形面积逼近曲线下的积分值。
以下是使用MATLAB编写的复化梯形公式的示例代码：```matlabfunction result = composite_trapezoidal(f, a, b, n)h = (b - a) / n; % 计算每个小区间的宽度% 计算每个小区间的积分值，并将其累加得到最终结果result = 0;for i = 1:nx_i = a + (i-1) * h; % 当前小区间的起点x_j = a + i * h; % 当前小区间的终点% 使用梯形公式计算当前小区间的积分值integral_i = (f(x_i) + f(x_j)) * h / 2;% 将当前小区间的积分值累加到总结果中result = result + integral_i;endend```在上述代码中，`f` 是要计算积分的函数，`a` 和 `b` 是积分区间的起点和终点，`n` 是将积分区间划分成的小区间数目。
你可以根据实际需求，将自己的函数替换到 `f` 的位置，并调用 `composite_trapezoidal` 函数来计算数值积分的近似值。
例如，假设要计算函数 `f(x) = x^2` 在区间 `[0, 1]` 上的数值积分，可以使用以下代码进行计算：```matlabf = @(x) x^2; % 定义要计算积分的函数a = 0; % 积分区间起点b = 1; % 积分区间终点n = 100; % 将积分区间划分为100个小区间result = composite_trapezoidal(f, a, b, n); % 使用复化梯形公式计算积分近似值disp(result); % 显示计算结果```运行上述代码，就可以得到函数 `f(x) = x^2` 在区间 `[0, 1]` 上的数值积分的近似值。
复化梯形公式和复化Simpson公式
数值计算方法上机题目3一、计算定积分的近似值：221x e xe dx =⎰ 要求：（1）若用复化梯形公式和复化Simpson 公式计算，要求误差限71021-⨯=ε，分别利用他们的余项估计对每种算法做出步长的事前估计；（2）分别利用复化梯形公式和复化Simpson 公式计算定积分；（3）将计算结果与精确解比较，并比较两种算法的计算量。
1.复化梯形公式程序：程序1（求f （x ）的n 阶导数：syms xf=x*exp(x) %定义函数f （x ）n=input('输入所求导数阶数:')f2=diff(f,x,n) %求f(x)的n 阶导数结果1输入n=2f2 =2*exp(x) + x*exp(x)程序2：clcclearsyms x%定义自变量xf=inline('x*exp(x)','x') %定义函数f(x)=x*exp(x)，换函数时只需换该函数表达式即可f2=inline('(2*exp(x) + x*exp(x))','x') %定义f(x)的二阶导数,输入程序1里求出的f2即可。
f3='-(2*exp(x) + x*exp(x))'%因fminbnd（）函数求的是表达式的最小值，且要求表达式带引号，故取负号，以便求最大值e=5*10^(-8) %精度要求值a=1 %积分下限b=2 %积分上限x1=fminbnd(f3,1,2) %求负的二阶导数的最小值点，也就是求二阶导数的最大值点对应的x值for n=2:1000000 %求等分数nRn=-(b-a)/12*((b-a)/n)^2*f2(x1) %计算余项if abs(Rn)<e %用余项进行判断break% 符合要求时结束endendh=(b-a)/n %求hTn1=0for k=1:n-1 %求连加和xk=a+k*hTn1=Tn1+f(xk)endTn=h/2*((f(a)+2*Tn1+f(b)))z=exp(2)R=Tn-z %求已知值与计算值的差fprintf('用复化梯形算法计算的结果 Tn=')disp(Tn)fprintf('等分数 n=')disp(n) %输出等分数fprintf('已知值与计算值的误差 R=')disp(R)输出结果显示：用复化梯形算法计算的结果Tn= 7.3891等分数n=7019已知值与计算值的误差R= 2.8300e-0082. Simpson公式程序：程序1：（求f（x）的n阶导数）：syms xf=x*exp(x) %定义函数f（x）n=input('输入所求导数阶数:')f2=diff(f,x,n) %求f(x)的n阶导数结果1输入n=4f2 =4*exp(x) + x*exp(x)程序2：clcclearsyms x%定义自变量xf=inline('x*exp(x)','x') %定义函数f(x)=x*exp(x)，换函数时只需换该函数表达式即可f2=inline('(4*exp(x) + x*exp(x))','x') %定义f(x)的四阶导数，输入程序1里求出的f2即可f3='-(4*exp(x) + x*exp(x))'%因fminbnd（）函数求的是表达式的最小值，且要求表达式带引号，故取负号，一边求最大值e=5*10^(-8) %精度要求值a=1 %积分下限b=2 %积分上限x1=fminbnd(f3,1,2) %求负的四阶导数的最小值点，也就是求四阶导数的最大值点对应的x值for n=2:1000000 %求等分数nRn=-(b-a)/180*((b-a)/(2*n))^4*f2(x1) %计算余项if abs(Rn)<e %用余项进行判断break% 符合要求时结束endendh=(b-a)/n %求hSn1=0Sn2=0for k=0:n-1 %求两组连加和xk=a+k*hxk1=xk+h/2Sn1=Sn1+f(xk1)Sn2=Sn2+f(xk)endSn=h/6*(f(a)+4*Sn1+2*(Sn2-f(a))+f(b)) %因Sn2多加了k=0时的值，故减去f(a)z=exp(2)R=Sn-z %求已知值与计算值的差fprintf('用Simpson公式计算的结果 Sn=')disp(Sn)fprintf('等分数 n=')disp(n)fprintf('已知值与计算值的误差 R=')disp(R)输出结果显示：用Simpson公式计算的结果Sn= 7.3891等分数n=24已知值与计算值的误差R= 2.7284e-008用复化梯形公式计算的结果为：7.3891，与精确解的误差为：2.8300e-008。
复化梯形公式和复化Simpson公式
数值计算方法上机题目3一、计算定积分的近似值：221x e xe dx =⎰ 要求：（1）若用复化梯形公式和复化Simpson 公式计算，要求误差限71021-⨯=ε，分别利用他们的余项估计对每种算法做出步长的事前估计；（2）分别利用复化梯形公式和复化Simpson 公式计算定积分；（3）将计算结果与精确解比较，并比较两种算法的计算量。
1.复化梯形公式程序：程序1（求f （x ）的n 阶导数：syms xf=x*exp(x) %定义函数f （x ）n=input('输入所求导数阶数:')f2=diff(f,x,n) %求f(x)的n 阶导数结果1输入n=2f2 =2*exp(x) + x*exp(x)程序2：clcclearsyms x%定义自变量xf=inline('x*exp(x)','x') %定义函数f(x)=x*exp(x)，换函数时只需换该函数表达式即可f2=inline('(2*exp(x) + x*exp(x))','x') %定义f(x)的二阶导数,输入程序1里求出的f2即可。
f3='-(2*exp(x) + x*exp(x))'%因fminbnd（）函数求的是表达式的最小值，且要求表达式带引号，故取负号，以便求最大值e=5*10^(-8) %精度要求值a=1 %积分下限b=2 %积分上限x1=fminbnd(f3,1,2) %求负的二阶导数的最小值点，也就是求二阶导数的最大值点对应的x值for n=2:1000000 %求等分数nRn=-(b-a)/12*((b-a)/n)^2*f2(x1) %计算余项if abs(Rn)<e %用余项进行判断break% 符合要求时结束endendh=(b-a)/n %求hTn1=0for k=1:n-1 %求连加和xk=a+k*hTn1=Tn1+f(xk)endTn=h/2*((f(a)+2*Tn1+f(b)))z=exp(2)R=Tn-z %求已知值与计算值的差fprintf('用复化梯形算法计算的结果 Tn=')disp(Tn)fprintf('等分数 n=')disp(n) %输出等分数fprintf('已知值与计算值的误差 R=')disp(R)输出结果显示：用复化梯形算法计算的结果Tn= 7.3891等分数n=7019已知值与计算值的误差R= 2.8300e-0082. Simpson公式程序：程序1：（求f（x）的n阶导数）：syms xf=x*exp(x) %定义函数f（x）n=input('输入所求导数阶数:')f2=diff(f,x,n) %求f(x)的n阶导数结果1输入n=4f2 =4*exp(x) + x*exp(x)程序2：clcclearsyms x%定义自变量xf=inline('x*exp(x)','x') %定义函数f(x)=x*exp(x)，换函数时只需换该函数表达式即可f2=inline('(4*exp(x) + x*exp(x))','x') %定义f(x)的四阶导数，输入程序1里求出的f2即可f3='-(4*exp(x) + x*exp(x))'%因fminbnd（）函数求的是表达式的最小值，且要求表达式带引号，故取负号，一边求最大值e=5*10^(-8) %精度要求值a=1 %积分下限b=2 %积分上限x1=fminbnd(f3,1,2) %求负的四阶导数的最小值点，也就是求四阶导数的最大值点对应的x值for n=2:1000000 %求等分数nRn=-(b-a)/180*((b-a)/(2*n))^4*f2(x1) %计算余项if abs(Rn)<e %用余项进行判断break% 符合要求时结束endendh=(b-a)/n %求hSn1=0Sn2=0for k=0:n-1 %求两组连加和xk=a+k*hxk1=xk+h/2Sn1=Sn1+f(xk1)Sn2=Sn2+f(xk)endSn=h/6*(f(a)+4*Sn1+2*(Sn2-f(a))+f(b)) %因Sn2多加了k=0时的值，故减去f(a)z=exp(2)R=Sn-z %求已知值与计算值的差fprintf('用Simpson公式计算的结果 Sn=')disp(Sn)fprintf('等分数 n=')disp(n)fprintf('已知值与计算值的误差 R=')disp(R)输出结果显示：用Simpson公式计算的结果Sn= 7.3891等分数n=24已知值与计算值的误差R= 2.7284e-008用复化梯形公式计算的结果为：7.3891，与精确解的误差为：2.8300e-008。
编程MATLAB程序实现复化梯形和辛普森数值积分
编程MATLAB程序实现复化梯形和辛普森数值积分MATLAB是一种高级编程语言和计算环境，适用于各种科学和工程应用。
在MATLAB中，可以使用数值积分的方法来近似计算函数的定积分。
本文将介绍如何使用MATLAB编程实现复化梯形和辛普森数值积分。
首先，我们来介绍复化梯形法。
复化梯形法是一种基本的积分数值方法，它将定积分区间等分为若干个小的子区间，然后在每个子区间上应用梯形公式进行近似计算。
下面是复化梯形法的MATLAB代码：``` matlabh=(b-a)/N;x=a:h:b;y=f(x);I = h * (sum(y) - (y(1) + y(end)) / 2);end```在上述代码中，`f`是积分的函数，`a`和`b`是积分的上下限，`N`是子区间的数量。
首先，我们计算出每个子区间的步长`h`，然后生成一个数组`x`，其中包含了每个子区间的起始点和终止点。
接下来，根据积分函数`f`计算出在每个子区间上的函数值，并将这些函数值存储在数组`y`中。
最后，使用梯形公式计算出近似积分结果`I`。
下面是使用复化梯形法进行数值积分的示例：``` matlaba=0;b = pi;N=100;disp(I);```接下来，我们来介绍辛普森法。
辛普森法是一种更精确的数值积分方法，它将定积分区间等分为若干个小的子区间，然后在每个子区间上应用辛普森公式进行近似计算。
下面是辛普森法的MATLAB代码：``` matlabh=(b-a)/(2*N);x=a:h:b;y=f(x);I = h / 3 * (y(1) + y(end) + 4 * sum(y(2:2:end-1)) + 2 * sum(y(3:2:end-2)));end```在上述代码中，`f`是积分的函数，`a`和`b`是积分的上下限，`N`是子区间的数量。
首先，我们计算出每个子区间的步长`h`，然后生成一个数组`x`，其中包含了每个子区间的起始点和终止点。