Implicit Finite difference 2D Heat

I'm currently working on a problem to model the heat conduction in a rectangular plate which has insulated top and bottom using a implicit finite difference method.

I've been using this document to help me http://www.geowiss.uni-mainz.de/Dateien/Finite_Differerence_Temp_2D.pdf although I am still confused on parts of the mathematics involved and writing the code

I have 2 main problems I would appreciate help with

1) The 'A' matrix I believe is supposed to have the diagonals filled with numbers whereas mine seems to have 'gaps' but i can't understand how to get rid of those gaps

2) I have fixed temperatures which i want to implement on the left and right hand side of the plate, which matrix would i input these temperatures in? I thought it would have been the rhs matrix

Answer 1

[Torsten]

1. The matrix A in equation (15) also has gaps as indicated by the two dots.

2. For fixed temperatures, add

T_1,j= T1_fix and T_nx,j = T2_fix

to the system of equations.

Best wishes

Torsten.