Comparison between the Jacobi and Gauss-Seidel methods for solving partial differential equations
Keywords:
linear partial differential equations, Jacobi method, Gauss-Seidel methodAbstract
This study aimed to search for a solution to linear partial differential equations, which represent many physical and engineering phenomena, and which only appear in the form of mathematical systems that describe the nature of these phenomena. The focus here was on the Laplace equation in the second dimension, as a model for describing these phenomena using the finite difference method. To approximate the solution of these equations, the equation is converted to another form, so that a linear system is obtained, which can be solved using one of the iterative methods. Among the methods used in this paper are the Jacobi and Gauss-Seidel methods, and it was found from what the numerical results showed that the Gauss method - Seidel is one of the best iterative methods to obtain a fast and approximate solution to the exact solution, which gives the lowest possible error
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