A study on a second order finite difference scheme for fractional advection–diffusion equations. Issue 2 (26th August 2018)

• Record Type: Journal Article
• Authors: Vong, Seakweng; Shi, Chenyang; Lyu, Pin
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 2(2019)
• Page Start: 493
• Page End: 508
• Publication Date: 2018-08-26
• Subjects: finite difference method -- fractional advection–diffusion equations -- second order scheme; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22310
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : Second order finite difference schemes for fractional advection–diffusion equations are considered in this paper. We note that, when studying these schemes, advection terms with coefficients having the same sign as those of diffusion terms need additional estimates. In this paper, by comparing generating functions of the corresponding discretization matrices, we find that sufficiently strong diffusion can dominate the effects of advection. As a result, convergence and stability of schemes are obtained in this situation.