Fourth order modified explicit decoupled group scheme in the solution of Poisson equation

Abstract

Abstract. The formulation and implementation of a new explicit group method in solving the two dimensional (2D) elliptic partial differential equation (PDE) is presented. The fourth order group scheme is derived from the rotated ninepoint finite difference discretization formula applied to the Poisson equation. Numerical solutions are obtained for different mesh sizes. The iterative procedure of the Fourth Order Modified Explicit Decoupled Group (FOMEDG) method is found to require lesser execution timings and iteration numbers compared to the existing Fourth Order Modified Explicit Group (FOMEG) method resulting in faster convergence rate.