The Splitting Extrapolation Method for Multidimensional Problems

Abstract

This note presents a splitting extrapolation process, which uses successively one-dimensional extrapolation procedure along only one variable with other variables kept fixed. This splitting technique is applied to the numerical cubature of multiple integrals, multidimensional integral equations and the difference method for solving the Poisson equation. For each case, the corresponding error estimates are given. They show the advantage of this method over the isotropic extrapolation along all the variables.