Relative and absolute error control in a finite-difference method solution of Poisson’s equation. (English)

Int. J. Math. Educ. Sci. Technol. 43, No. 5, 684-694 (2012).

Summary: An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson’s equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm, which are mainly due to its second-order nature. A generalization of the algorithm for finite-difference methods of arbitrary order is presented. We believe that the algorithm is a valuable addition to typical textbook discussions of the five-point finite-difference method for Poisson’s equation.