Abstract:
Numerical iterative methods are applied for the solution of two dimensional Elliptic partial differential equations such as laplace's and poisson's equations. these kinds of differential equations have specific applications models of physics and engineering. The distinct
approximation of the two equations is founded upon the theory of finite difference. In this work, the approximation of five point's scheme of finite difference method is used for the
equations of Laplace and Poisson to get linear system of equations. The solution of these
Dirichlet boundary is discussed by finite difference method. An elliptic PDE transforms the
PDE into a system of algebraic equations whose coefficient matrix has a tri-diagonal block
format, using the finite difference method. Numerical iterative methods such as Jacobi
method and Gauss-Seidel method are used to solve the resulting finite difference
approximation with boundary conditions.
