Gauss-Seidel Iteration Method with Finite Difference Approach in MATLAB

This MATLAB program implements a numerical solution for differential equations by combining the finite difference method with Gauss-Seidel iteration. The finite difference approach discretizes the continuous differential equation into a system of linear algebraic equations by approximating derivatives using difference quotients on a predefined grid. The Gauss-Seidel iterative method then solves this linear system efficiently by sequentially updating each variable using the most recent values, which typically provides faster convergence compared to Jacobi iteration. The implementation includes key components such as grid generation, boundary condition handling, coefficient matrix formation, and convergence criteria checking. The algorithm particularly excels in solving elliptic partial differential equations commonly encountered in heat transfer analysis, fluid dynamics simulations, and potential field problems. Users can modify parameters including grid resolution, convergence tolerance, and maximum iteration counts based on specific application requirements. The complete source code, example configurations, and documentation are packaged in the downloadable archive "matlab_finite_difference_gauss_seidel.rar". The program structure allows easy adaptation to various boundary value problems by modifying the discrete differential operators and boundary condition implementations.