MATLAB Matlab program using implicit Finite Difference

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The discussion centers on creating a MATLAB program to solve a heat transfer problem using an implicit method. The user seeks assistance in formulating a tridiagonal matrix to solve for temperature T(i,n) based on the temperatures at three preceding nodes. The problem involves discretizing a partial differential equation (PDE) with dimensionless variables, where both time and spatial dimensions range from 0 to 1. The user mentions the need to apply the Thomas Algorithm for solving the tridiagonal matrix. Additional details provided include the discretization parameters Δn for time and Δi for space, with a defined relationship λ = Δt/Δx².
tactical
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Hello,

I need help writing a MATLAB program to solve a heat transfer problem implicitly. For some reason this is very confusing to me. The problem is stated below. Any help is greatly appriciated. Let me know if you need a little more info.

I need to write a program to solve this problem. I want to solve for a temperature T(i,n) using the temperature at the 3 nodes ahead of it. Essentially it's going to be a tridiagonal matrix in which you can solve using Thomas Algorithm. I just need help writing a program to get this tridiagonal matrix.
2h2leud.jpg


Edit: Also, all variable are dimensionless, therefore time goes from 0 to 1 and x also goes from 0 to 1. time is broken up into Δn parts and x is broken up into Δi parts. λ = Δt/Δx2
 
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I guess this might help some:

This what the PDE that was discretized

xdv71l.png
 

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