Explicit Eulers Method for time advancement

Question

Cassidy Holene 2021-2-22

0
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https://ww2.mathworks.cn/matlabcentral/answers/752874-explicit-eulers-method-for-time-advancement

回答： Alan Stevens 2021-2-22

Hello I am trying to use explicit Euler for time advancement and the second-order centraldifference scheme for the spatial derivative, solve the equation to steady

state on a uniform grid. Plot the exact and numerical steady solutions for Nx = 10, 20.

𝜕𝑇/𝜕𝑡 = 𝛼*( 𝜕^2𝑇/𝜕𝑥^2) + 𝑆(𝑥) on the boundary of 0 ≤ 𝑥 ≤ 𝐿𝑥 The initial and boundary conditions are 𝑇(𝑥, 0) = 0 𝑇(0,𝑡) = 0 𝑇(𝐿𝑥,𝑡) = 𝑇steady(𝐿𝑥) Take 𝛼 = 1, 𝐿𝑥 = 15, and 𝑆(𝑥) = −(𝑥 2 − 4𝑥 + 2)𝑒 −𝑥 . The exact steady solution is 𝑇steady(𝑥) = 𝑥 2𝑒 −𝑥

heres the code I have can someone explain where I went wrong

alpha =0;
x = 0;
n =10;
T(0)4ess = 0;
h=0.1;
s(x)=-(x^2-4*x+2)*exp^(-x);
for i=1:n
    T(i+1)=T(i) + h;
    T(i)^(n+1)=T(i+1)^n+((alpha*h)/(x+h)^2)*(T(i+1)^n-2T(i)^n+T(i-1)^n)+h*s(x);
    x = x +1;
    h = h +0.1;
end
plot(x,T);
grid on;