Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method

Abstract

The method of lines (MOL) is a solution procedure for solving partial differential equation (PDE) and the Crank-Nicholson method (CNM) is an implicit finite difference method, used to solve the elliptic equation and similar partial differential equations numerically. In this study, the numerical techniques were introduced to solve elliptic partial differential equation (PDE) together with initial and boundary conditions. The Poisson equation was considered as an elliptic PDE. Particularly, two methods were used to solve a two-dimensional Poisson equation numerically, such as the method of lines (MOL) and Crank-Nicholson method (CNM). The implementation of the solutions was done using Microsoft office spreadsheet and MATLAB programing language. Lastly, the numerical solutions were presented graphically which was obtained with method of lines along with Crank-Nicholson method.