Acceleration of the Convergence in Finite Difference Method by Predictor-Corrector and Splitting Extrapolation Methods

Abstract

Two types of combination methods for accelerating the convergence of the finite difference method are presented. The first is based on an interpolation principle (correction method) and the second one on extrapolation principle. They improve the convergence form $O(h^2)$ to $O(h^4)$. The main advantage when compared with standard methods, is that the computational work can be split into independent parts, which can be carried out in parallel.