Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

Abstract

A new three-level rotated implicit method for solving the two-dimensional time fractional diffusion-wave equation AIP Conference Proceedings 1974, 020018 (2018 030003 (2016) At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 030003-7Group Abstract.Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a twodimensional time fractional diffusion equation. These methods were derived from the standard and rotated CrankNicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number.

Fast O(N) hybrid Laplace transform-finite difference method in solving 2D time fractional diffusion equation

“…There are various finite difference methods such as explicit and implicit schemes that can be used to solve problem (1.1) with a particular approximation formula for the Caputo fractional derivative. Here, we recall a standard Crank-Nicolson finite difference scheme proposed by Balasim and Ali [2] for solving problem (1.1) to compare it with the proposed hybrid method in the previous section. Utilizing the discretization formula in [15] to approximate the time fractional derivative in Eq.…”

An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis

“…In order to fix this problem and accelerate the convergence, we use the explicit decoupled group (EDG) method introduced by Abdullah in 1990 [22]. Many studies have been done in reference to the EDG method for examples [23][24][25][26]. The EDG method is based on rotating the Crank-Nicolson difference scheme and group ordering of grid points.…”

A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

“…High-order schemes produce more accurate results, but suffer from slow convergence due to the increase of complexity in the algorithm. Since explicit group methods reduce algorithm complexity [28][29][30][31], we propose the use of explicit group method for the solution of two-dimensional Rayleigh-Stokes problem for a heated generalized second-grade fluid. The main purpose of this article is to solve two-dimensional Rayleigh-Stokes problem with the high-order explicit group method (HEGM).…”