The use of Richardson extrapolation to reduce the truncation error in the finite difference solution of one and two dimensional electrostatics problems

Abstract

Richardson extrapolation can be used to obtain an accurate solution to a problem while being efficient with both computer time and memory. In this paper, Richardson extrapolation is used in conjunction with the finite difference method to solve both one- and two-dimensional electrostatics problems. Numerical results are presented for both cases, and it is seen that high accuracy can be achieved.