Finite Difference Method to find Steady State

Hello experts,

I have to solve the following equation to find a converged solution.

At i=0, T=10 and at i=5, T=50. (n=5)

I want to get the converged solution of T at i=2, 3, 4.

I'm fairly comfortable with MATLAB but this is the first time that I'm using MATLAB for these kind of mathematical approach and I'm learning completely alone, relying on online materials.

How should I approach this? I'd appreciate your recommendations, reading materials, suggestions and/or pointers rather than a complete code at this point.

I know the question is vague but I'd welcome any suggestions for starting points :)

TIA!

[Torsten]

What are the values for T_i^n for n =0 ?

[James]

Apologies, I've missed including that info properly.

When n=0, T_i^(n+1)=10, 73, 100, 85, 50 respectively at i=1, 2, 3, 4, 5.

[Ragul Kumar]

Hello experts,

I am trying to solve the finite difference methof for crank nicolson scheme to 2d heat equation. please let me know if you have any MATLAB CODE for this

Boundary codition are

If you can kindly send me the matlab code, it will be very useful for my research work . thank you very much.

Answer 1

[Torsten]

T = zeros(6,5);
T(1:6,1) = 10;
T(1:6,5) = 50;
T(1,2) = 73;
T(1,3) = 100;
T(1,4) = 85;
for n=1:5
  for i =2:4
     T(n+1,i) = T(n,i) + 0.3*(T(n,i+1)-2*T(n,i)+T(n,i-1));
  end
end
T

[darova]

[Torsten]

Thank you for formatting. Unfortunately, I can't use the editor options at the screen I'm currently working on.

[James]

This works!

However, I noticed that I haven't stated my question correctly. To find the converged solution, equation has to be iterated until the steady state approaches. I will start a new thread, properly stating the question.

Edit: I posted the question again, hopefully it makes more sense now.

https://www.mathworks.com/matlabcentral/answers/516506-finite-difference-method-to-find-steady-state

[Torsten]

Either choose a larger value than 5 for n or solve directly the linear system dT/dt = 0, i.e.

T(1) = 10

T(i+1) - 2*T(i) + T(i-1) = 0 (i=2,3,4)

T(5) = 50

[James]

Thank you, Torsten. I think that was what I wanted. It was my fault that I didn't post the question correctly :)

I'm still learning and I will try your suggestion.