CN-WSGD schemes and CN-EWSGD schemes for space-fractional advection-diffusion equations

Abstract

We consider high order finite difference schemes for one-dimensional space-fractional advection-diffusion equation (SFADE). The temporal derivative is approximated by the Crank-Nicolson (CN) scheme and the space fractional derivatives are approximated by the weighted and shifted Gr\”{u}nwald difference (WSGD) scheme. In general WSGD schemes have second order accuracy, and by selecting a special parameter, we get the third order accuracy scheme. However, the third order scheme may not be stable. In this talk, some results on the accuracy and the stability of CN-WSGD schemes are reported.

Biography

Prof. Lin is a professor of Department of Mathematics, Shantou University, China. He got his PhD degree in Hong Kong University in 1995. His research area include numerical linear algebra, fast algorithms for Toeplitz matrix, numerical methods for PDEs.