Search

This paper aims to propose a high-order and accurate numerical scheme for the solution of the nonlinear diffusion equation with Riesz space fractional derivative. To this end, we first discretize the Riesz fractional derivative with a fourth-order finite difference method, then we apply a boundary value method (BVM) of fourth-order for the time integration of the resulting system of ordinary differential equations. The proposed method has a fourth-order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of BVM. The numerical results are compared with analytical solutions and with those provided by other methods in the literature. Numerical experiments obtained from solving several problems including fractional Fisher and fractional parabolic-type sine-Gordon equations show that the proposed method is an efficient algorithm for solving such problems and can arrive at the high-precision. [ABSTRACT FROM AUTHOR]

In this paper, a new numerical technique is presented for the solution of two-dimensional time fractional subdiffusion equation. To this end, we use the Galerkin spectral element method to discretize the spatial derivatives, weighted and shifted Grünwald difference (WSGD) operator to discretize the fractional term and for the time stepping, an alternating direction implicit (ADI) method based on the Crank-Nicolson scheme is investigated. The unconditionally stability of the proposed method as well as an error estimate for the full discretization scheme are presented. Numerical results are reported to support the theoretical analysis and to show the accuracy and efficiency of proposed method in comparison with other ADI schemes. [ABSTRACT FROM AUTHOR]

The aim of this work is to propose an efficient numerical method for the solution of two‐dimensional multiterm time fractional diffusion‐wave equation. The Caputo time fractional derivatives of equation are approximated by a scheme of order O(τ3−α), 1<α<2. To obtain a full‐discrete scheme, we apply the Legendre spectral element method on the spatial direction. Unconditional stability of the semidiscrete scheme and error estimate of full‐discrete method is presented. Numerical experiments are carried out to demonstrate the accuracy of the proposed method and to compare the results with the numerical solutions of other schemes in the literature. The results show that the present method is accurate and efficient. It is illustrated that the numerical results are in good agreement with theoretical ones. [ABSTRACT FROM AUTHOR]