Abstract and Applied Analysis
Volume 2013 (2013), Article ID 763630, 10 pages
http://dx.doi.org/10.1155/2013/763630
Research Article

General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems

Xiaohan Long1 and Chuanjun Chen2

1Department of Mathematics and Information, Ludong University, Yantai 264025, China
2Department of Mathematics and Information Science, Yantai University, Yantai 264005, China

Received 18 October 2012; Accepted 7 December 2012

Academic Editor: Xinguang Zhang

Copyright © 2013 Xiaohan Long and Chuanjun Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The general formulation of the second-order semi-Lagrangian methods was presented for convection-dominated diffusion problems. In view of the method of lines, this formulation is in a sufficiently general fashion as to include two-step backward difference formula and Crank-Nicolson type semi-Lagrangian schemes as particular ones. And it is easy to be extended to higher-order schemes. We show that it maintains second-order accuracy even if the involved numerical characteristic lines are first-order accurate. The relationship between semi-Lagrangian methods and the modified method of characteristic is also addressed. Finally convergence properties of the semi-Lagrangian finite difference schemes are tested.