NUMERICAL METHODS FOR THE VARIABLE-ORDER FRACTIONAL ADVECTION-DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

NUMERICAL METHODS FOR THE VARIABLE-ORDER FRACTIONAL ADVECTION-DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractiona...

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Veröffentlicht in:SIAM journal on numerical analysis 2009-01, Vol.47 (3), p.1760-1781
Hauptverfasser: ZHUANG, P., LIU, F., ANH, V., TURNER, I.
Format: Artikel
Sprache:eng
Schlagworte:
Advection-diffusion equation
Applied mathematics
Approximation
Boundary conditions
Convergence
Copyright
Differential equations
Error rates
Extrapolation
Mathematical analysis
Mathematical extrapolation
Methods
Nonlinearity
Numerical analysis
Numerical methods
Parameter estimation
Partial differential equations
Perceptron convergence procedure
Random walk
Solute movement
Stability
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Zusammenfassung:In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
ISSN:0036-1429
1095-7170
DOI:10.1137/080730597