Abstract
AbstractIn many areas of science and engineering, to determine the steady-state temperature, potential distribution, electricity, gravitation, Laplace and Poisson elliptic partial differential equation is required to solve. It is difficult to obtain an analytical solution of most of the partial differential equations that arise in mathematical models of physical phenomena. So, five-point finite difference method (FDM) is used to solve the two-dimensional Laplace and Poisson equations on regular (square) and irregular (triangular) region. To solve partial differential equation, specific boundary conditions are required. In this study, Dirichlet and Robin boundary conditions are considered for solving the system of equations at each iteration. When the function itself is specified, the boundary is called Dirichlet boundary. In some problems, a linear combination of function and its normal derivative is specified on the boundary, called Robin boundary. The obtained numerical results are compared with analytical solution. The study objective is to check the accuracy of FDM for the numerical solutions of square and triangular bodies of 2D Laplace and Poisson equations.KeywordsFinite difference methodDirichlet boundary conditionRobin boundary conditionLaplace equationPoisson equation
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