Euler's method to solve the heat equation

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Kevser Cifci 2022-1-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1631505-euler-s-method-to-solve-the-heat-equation

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hello,

I want to plot the exact and proximative curves for the solution of the heat equation here

but my code has a problem:

x1=0;
a = 1; 
x2=a;
T = 1; % length of time for solution
n = 599;   
N = 150;
dx = a/(n+1.); 
dt = T/N; 
t=0.; % initial time = 0
beta = 1.e-5; 
s = beta*dt/(dx^2);  
if s > 0.5
   fprintf('gain parameter > 0.5');
end
Adiag = (1-2*s)*ones(n,1);
Asubs = s*ones(n,1);
Asuper = s*ones(n,1);
A = spdiags([Asubs,Adiag,Asuper],[-1 0 1],n,n);
A(n,n) = 1-s;
b= zeros(n,1);
b(1) = 0;
b(n) =  0;
x = linspace(0,a, n+1)';
f=inline('sin(pi*x)');
U_tk = f(x);
a=1 ;
v = inline('exp(-a^2*pi*t)*sin(pi*x)','x','t','a'); % exact solution 
for n=1:N
    plot(x,U_tk,'b',x,v(x,t,a),'r')
    axis([0,1.5,-0.5, 1.5])
    title(['lambda=',num2str(s)])
    pause,
end;