POISSON EQUATION FOR ELECTROSTATIC FIELD USING THE FINITE DIFFERENCE METHOD - IFFAH FATHANAH, AHMAD RAZALI (Universiti Malaysia Sarawak, (UNIMAS), 2019)
Elliptic partial differential equation is a boundary value problem which can be thought as the stable of an evolution problem. There are two type equations that fall under elliptic boundary value problem that is Poisson and Laplace equation. Poisson equation is very useful in solving few problems in ordinary world such as heat physical phenomenon, incompressible flow, electricity potential and static physical property. This paper will concentrate on solving one problem; that is modelling Poisson Equation for electrostatic field. It is a useful approach to the calculation to relate the charge density by the divergence relationship. The basic main equations are derived directly so that the algorithm can be extended from the classical Poisson equation to the generalized Poisson equation in order to include the effects of varying dielectrics within the domain. The Dirichlet boundary will be use because it is nothing more than a forced solution to the potential function at specific points. This problem will be solved via matrix and successive over relation to get a good solution for the implementation result.