Matlab program using implicit Finite Difference

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SUMMARY

The discussion focuses on creating a MATLAB program to solve a heat transfer problem using implicit finite difference methods. The user seeks assistance in constructing a tridiagonal matrix to apply the Thomas Algorithm for solving temperature values T(i,n) based on the temperatures at three preceding nodes. The problem involves dimensionless variables, with time and space discretized into Δn and Δi parts, respectively, and the relationship λ = Δt/Δx² is highlighted as a key factor in the discretization process.

PREREQUISITES
  • Understanding of MATLAB programming
  • Knowledge of implicit finite difference methods
  • Familiarity with tridiagonal matrices and the Thomas Algorithm
  • Basic concepts of heat transfer and partial differential equations (PDEs)
NEXT STEPS
  • Research MATLAB's built-in functions for matrix operations
  • Learn about the implementation of the Thomas Algorithm in MATLAB
  • Study implicit finite difference methods for solving PDEs
  • Explore examples of heat transfer problems solved using MATLAB
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Engineers, researchers, and students involved in computational heat transfer, MATLAB programmers, and anyone interested in numerical methods for solving partial differential equations.

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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