Solving 2D Time-Fractional Diffusion Equations by Preconditioned Fractional EDG Method

Abdulkafi Mohammed Saeed

Abdulkafi Mohammed Saeed Associate Professor at Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Keywords: Preconditioned Fractional Explicit Decoupled Group Method; Time-Fractional Diffusion Equation

Abstract

Fractional differential equations play a significant role in science and technology given that several scientific problems in mathematics, physics, engineering and chemistry can be resolved using fractional partial differential equations in terms of space and/or time fractional derivative. Because of new developments in the analysis and understanding of many complex systems in engineering and sciences, it has been observed that several phenomena are more realistically and accurately described by differential equations of fractional order. Fast computational methods for solving fractional partial differential equations using finite difference schemes derived from skewed (rotated) difference operators have been extensively investigated over the years. The main aim of this paper is to examine a new fractional group iterative method which is called Preconditioned Fractional Explicit Decoupled Group (PFEDG) method in solving 2D time-fractional diffusion equations. Numerical experiments and comparison with other existing methods are given to confirm the superiority of our proposed method.

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References

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