Exact and Numerical Solutions of Poisson Equationfor Electrostatic Potential Problems

It is well known that there are many linear and nonlinear partial equations in various fields of science and engineering. The solution of these equations can be obtained by many different methods. In recent years, the studies of the analytical solutions for the linear or nonlinear evolution equations have captivated the attention of many authors. The numerical and seminumerical/analytic solution of linear or nonlinear, ordinary differential equation or partial differential equation has been extensively studied in the resent years. There are several methods have been developed and used in different problems 1-3 . The homotopy perturbation method is relatively new and useful for obtaining both analytical and numerical approximations of linear or nonlinear differential equations 4-7 . This method yields a very rapid convergence of the solution series. The applications of homotopy perturbation method among scientists received more attention recently 8-10 . In this study, we will first concentrate on analytical solution of Poisson equation, using frequently in electrical engineering, in the form of Taylor series by homotopy perturbation method 11-13 . The boundary element method is a numerical technique to solve boundary value problems represented by linear partial differential equations 14 and has some important