Penerapan Skema Jacobi dan Gauss Seidel pada Penyelesaian Numerik Persamaan Poisson

Abstract

Differential equations are equations that involve an unknown function and derivatives.There will be times when solving the exact solution for the equation may be unavailable. At these times explicitand implicit methods will be used in place of exact solution.By manipulating such methods, one can find ways to provide goodapproximations compared to the exact solution.In some cases, manipulating such methods leads to a linear equation systems. The Jacobi and Gauss-Seidel method are two of the most famous numerical method for solving linear equation systems The diagonal dominance of the matrix is necessary condition before applying both methods. In this paper, we implement Jacobi and Gauss-Seidel methods for solving Poisson equation. We use literature study to investigate the problem. Some numerical experiments in various step size are given to show the difference of both methods on their computation time and number of iteration. From numerical experiments, it is shown that choosing step size influences both the computation time and number of iteration.