抛物型初边值问题的matlab求解

%Divide the grid

dx=0.1;dt=0.001;

r=0.1;a=1;

n=(1/dx)-1;

I=eye(n-1);

%Creat C matrix

for i=1:n-2

C(i,i+1)=1;

end

for i=2:n-1

C(i,i-1)=1;

end

%Accumulate D

D=(1-2*r*a)*I+r*a*C;

%Creat Vector

for i=2:n-1;

a(i)=D(i,i-1);

end

for i=1:n-1;

b(i)=D(i,i);

end

for i=1:n-2;

c(i)=D(i,i+1);

end

% Perform D=LU

u(1) = b(1);

for i = 2:n-1

l(i) = a(i)/u(i-1);

u(i) = b(i) - l(i) *c(i-1);

end

% Ly = d

y(1) = d(1);

for i = 2:n-1

d(i)=x(i-1);

y(i) = d(i)-l(i)*y(i-1);

end

% Ux = y

x(1) = y(1);

x(n-1) = y(n-1)/u(n-1);

for i = n-2:-1:1

x(i) = (y(i)-c(i)*x(i+1))/u(i); end