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

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  • Xiaohan Long
  • Chuanjun Chen

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.

Suggested Citation

  • Xiaohan Long & Chuanjun Chen, 2013. "General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, January.
    • Handle: RePEc:hin:jnlaaa:763630
    DOI: 10.1155/2013/763630
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