Electrostatic Potential Distribution by Numerical Method Alternating Direction Implicit Method

Charge free electrostatic potential has been calculated from Laplace equation with specific boundaries. Laplace equation is second-order partial differential equation (PDE) widely useful in physics because its solutions occur in problems of electrical, magnetic, and gravitational potentials, of steady-state temperatures, of hydrodynamics and of stress distribution. Solution of Partial Differential Equations (PDEs) is virtually impossible to obtain analytical solution. So, numerical methods are used to approximate the solution of such type of partial differential equation. The Alternating Direction Implicit (ADI) method has been used to solve the two-dimensional Laplace equations on regular (square and rectangular) region with Dirchlet boundary conditions. ADI method is an iterative and unconditionally stable method which is a popular method for solving the large matrix equations that arise in system theory and control theory. The obtained numerical results are compared with analytical solution as well as finite difference method. The results have been shown the better accuracy of ADI method than the finite difference method. The study objective is to check the accuracy of ADI method for the numerical solutions of two-dimensional Laplace equations for calculating potential distribution.