analytic solution with infinite sum

Question

Chien-Cheng Chiu 2020-2-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507120-analytic-solution-with-infinite-sum

回答： darova 2020-2-23

Hi,

I am having trouble figuring out how to write the code for this function that contains an infinite series.

Ti = 150;
T1 = 300;
T2 = 200;
L = 1;
alpha = 0.1;
delta_x = 0.05;
delta_t = 0.01;
N_time = 51;
N_space = 21;
x = linspace(0,L,N_space);
t = linspace(0,0.5,N_time);

I need to make the code so that it can compute this:

% I also need a little help in making the function. I have used syms m x t, but it doesn't work all the time.
c_m = (2/m*pi) ((Ti - T1)-(-1)^m*(Ti - T2))
T(x,t) = T1 + (T2 - T1)*(x/L) + %my unknown part: the infinite sum starting from 1 of c_n*exp(-m^2*pi^2*alpha*t/L^2)*sin(m*pi*x/L)

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darova 2020-2-23

Can you please write formula in LaTeX format?

Something like this:

Chien-Cheng Chiu 2020-2-23

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Answer 1

darova 2020-2-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507120-analytic-solution-with-infinite-sum#answer_416985

在 MATLAB Online 中打开

Here is my attempt

Ti = 150;
T1 = 300;
T2 = 200;
L = 1;
alpha = 0.1;
delta_x = 0.05;
delta_t = 0.01;
N_time = 51;
N_space = 21;
x = linspace(0,L,N_space);
t = linspace(0,0.5,N_time);
[X,T] = meshgrid(x,t);
cm = X*0;
for m = 1:100
    C1 = 2/m/pi*( (Ti-T1)-(-1)^m*(Ti-T2) );
    C2 = exp(-m^2*pi^2*alpha*T/L^2).*sin(m*pi*X/L);
    cm = cm + C1*C2;
end
surf(X,T,cm)
xlabel('X')
ylabel('T')