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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… (More)

(2008) New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source: Abstract. A… (More)

A Fourier method for the fractional diffusion equation describing sub-diffusion. Abstract In this paper, a fractional partial differential equation (FPDE) describing sub-diffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the… (More)

In this paper, two finite difference/element approaches for the time-fractional sub-diffusion equation with Dirichlet boundary conditions are developed, in which the time direction is approximated by the fractional linear multistep method and the space direction is approximated by the finite element method. The two methods are unconditionally stable and… (More)

(2009) Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation. Abstract In this paper, we consider the variable-order nonlinear fractional diffusion equation ∂u(x, t) ∂t = B(x, t) x R α(x,t) u(x, t) + f (u, x, t), where x R α(x,t) is a generalized Riesz fractional derivative… (More)

Approximation of the Levy–Feller advection–dispersion process by random walk and finite difference method. Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source: Abstract In this paper we present a… (More)

In this paper, a new alternating direction implicit Galerkin–Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank–Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly… (More)