Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
نویسندگان
چکیده
منابع مشابه
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. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Som...
متن کاملNumerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term
In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Fina...
متن کاملEuler/Quasi-wavelet method for the variable order fractional advection-diffusion equation with a nonlinear source term
Abstract: New numerical techniques are presented for the solution of a class of the variable order fractional advection-diffusion equation with a nonlinear source term on one-dimensional finite domain. Quasiwavelet and double quasi-wavelet are used for the spatial discretization. For the time stepping, Euler method is considered. We also tested the method proposed on several problems with very ...
متن کاملNumerical Solving Two-dimensional Variable-order Fractional Advection-dispersion Equation
Abstract: In this paper, a two-dimensional variable-order fractional advection-dispersion equation with variable coefficient is considered. The numerical method with first order temporal accuracy and first order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by using energy method. Finally, the results of a numerical example supports the theoret...
متن کاملNumerical techniques for the variable order time fractional diffusion equation
(2012) Numerical techniques for the variable order time fractional diffusion equation. NOTICE: this is the author's version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2009
ISSN: 0036-1429,1095-7170
DOI: 10.1137/080730597