I see that you're trying to plot the general solution you have found but the equation given and the equation in the code don't match. The equation in the code does not contain the "T0/2" term.Furthermore, from the described desired result, I think the "T0/2" inside the summation is a mistake. I edited the code to get a plot that looks similar to the desired result.
% MATLAB code to plot temperature with y on the y-axis and x on the x-axis
% Define constants
T0 = 1; % Maximum temperature
L = 1000; % Period length
n_max = 10000; % Maximum number of terms in the Fourier series
% Define the ranges for x and y
x = linspace(0, 1000, 50); % x from 0 to 2
y = linspace(0, 5 * L, 500); % y from 0 to 5L
% Initialize the figure
figure;
hold on;
% Loop through values of x
%Marked section starts
for ix = 1:length(x)
T = zeros(size(y)); % Initialize the temperature array for the current x
% Calculate temperature for each y using Fourier series
for n = 1:2:n_max % Only odd n
bn = 2 * T0 / (pi * n); % Fourier coefficient
% Calculate the temperature for the current y and x
T = T + bn * sin(2 * pi * n * y / L) .* exp(-2 * pi * n * x(ix) / L);
end
T = T + T0/2;
% Plot the temperature against y for the current x
plot(y, T, 'DisplayName', sprintf('x = %.2f', x(ix)));
end
%Marked section ends
% Customize the plot
xlabel('y (Position along the boundary)');
ylabel('Temperature T(x, y)');
title('Temperature Waves Decaying with Increasing x');
grid on; % Add grid for better visualization
legend show; % Show legend for different x values
hold off;
Hope this helps!
