Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term | Zendy

Peixian Zhuang | Zendy; F. Liu | Zendy; Vo Anh | Zendy; Ian Turner | Zendy

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Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

Author(s) -

Peixian Zhuang,

F. Liu,

Vo Anh,

Ian Turner

Publication year - 2009

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/080730597

Subject(s) - mathematics , term (time) , nonlinear system , mathematical analysis , diffusion equation , stability (learning theory) , advection , convergence (economics) , extrapolation , variable (mathematics) , convection–diffusion equation , fractional calculus , physics , quantum mechanics , economics , thermodynamics , economy , machine learning , economic growth , computer science , service (business)

In this paper, we consider a variable-order fractional advection-diffusion equation\udwith a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the\udequation are proposed. Stability and convergence of the methods are discussed. Moreover, we also\udpresent a fractional method of lines, a matrix transfer technique, and an extrapolation method for\udthe equation. Some numerical examples are given, and the results demonstrate the effectiveness of\udtheoretical analysis.\u

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