Premium
A study on a second order finite difference scheme for fractional advection–diffusion equations
Author(s) -
Vong Seakweng,
Shi Chenyang,
Lyu Pin
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22310
Subject(s) - advection , mathematics , discretization , diffusion , convergence (economics) , stability (learning theory) , order (exchange) , sign (mathematics) , convection–diffusion equation , mathematical analysis , finite difference method , finite difference , physics , computer science , finance , machine learning , economics , thermodynamics , economic growth
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.