# Finite Difference Method to find Steady State

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Jake il 8 Apr 2020
Commentato: Ragul Kumar il 6 Nov 2020
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!
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Jake il 8 Apr 2020
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 il 6 Nov 2020
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.

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### Risposta accettata

Torsten il 8 Apr 2020
Modificato: Torsten il 9 Apr 2020
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
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Torsten il 9 Apr 2020
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
Jake il 9 Apr 2020
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.

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