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Solution of a Tridiagonal System of Linear Equations

UPDATED: 01/22/2025

This workbook solves a simple one-dimensional, steady-state conduction equation by finite-difference methods.  Such a system results in a tridiagonal system of linear equations.  The left side of this plane wall is adiabatic by symmetry; the right side is exposed to convection.  This workbook demonstrates the solution of the coupled set of equations by a simple iteration scheme.  It also implements a direct solution of the tridiagonal system using a VBA version of the LAPACK routine for tridiagonal systems (SGTSV).

Temperature vs. distance in a plane wall corresponding to conduction with volumetric heat generation. The plots include: 1. the analytical solution, 2. a finite-difference solution where the equations are solved by iteration, and 3. finite-difference solution where the tridiagonal system of linear equations is solved directly by Gauss-elimination.

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