الحل التقريبي لمعادلة بواسون غير الخطية بطريقة هوموتوبي-العناصر المنتهية FE-HM

Abstract EN

The main aim to this research is to find the approximation solution of the nonlinear Poisson equation by combining the finite element method FEM with homotopy analysis method HAM in a single approximation method because the finite element method needs when applied to nonlinear partial differential equations either for iterative methods such as ( Newton_Gauss Method14, Picard's iterative method3, Newton_Galarkin Method4) or for other approximation methods such as(B_Splain24, Homotopy Analysis6).

In this article, the finite element method was combined with the Homotopy analysis method with one method called Homotopy _Finite Element Method FE_HM, to convert the nonlinear matter into a linear matter through the HAM method, and to overcome the engineering complexity of the region by a grid of finite elements through the FEM method, We obtained good results when applying this method to the nonlinear Poisson equation on Dirichlet boundary condition, and this method was programmed through the Matlab program.