Analysis on Two Approaches for High Order Accuracy
Finite Difference Computation

November 16, 2011

Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Xinyu Geng
School of Computaer Science
Southwest Petroleum University
Chengdu, Sichuan 610600, China

Ruxin Dai
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Abstract

We analyze two approaches for enhancing the accuracy of the standard second order finite difference schemes in solving one dimensional elliptic partial differential equations. These are the fourth order compact difference scheme and the fourth order scheme based on the Richardson extrapolation techniques. We study the truncation errors of these approaches and comment on their regularity requirements and computational costs. We present numerical experiments to demonstrate the validity of our analysis.


Download the PDF file zhang12a.pdf.
Applied Mathematics Letters, Vol. 25, 2081-2085 (2012).