Error Estimates of Finite Difference Methods for the Fractional Poisson Equation with Extended Nonhomogeneous Boundary Conditions
Year: 2023
Author: Xinyan Li
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 194–212
Abstract
Two efficient finite difference methods for the fractional Poisson equation involving the integral fractional Laplacian with extended nonhomogeneous boundary conditions are developed and analyzed. The first one uses appropriate numerical quadratures to handle extended nonhomogeneous boundary conditions and weighted trapezoidal rule with a splitting parameter to approximate the hypersingular integral in the fractional Laplacian. It is proven that the method converges with the second-order accuracy provided that the exact solution is sufficiently smooth and a splitting parameter is suitably chosen. Secondly, if numerical quadratures fail, we employ a truncated based method. Under specific conditions, the convergence rate of this method is optimal, as error estimates show. Numerical experiments are provided to gauge the performance of the methods proposed.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.070422.220922
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 194–212
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Fractional Poisson equation finite difference method nonhomogeneous boundary condition error estimates integral fractional Laplacian.