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Appl. Sci. 2018, 8(6), 960; https://doi.org/10.3390/app8060960

A Finite Difference Method on Non-Uniform Meshes for Time-Fractional Advection–Diffusion Equations with a Source Term

Department of Mathematics and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Messina, Italy
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Received: 8 May 2018 / Revised: 1 June 2018 / Accepted: 7 June 2018 / Published: 12 June 2018
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Abstract

The present paper deals with the numerical solution of time-fractional advection–diffusion equations involving the Caputo derivative with a source term by means of an unconditionally-stable, implicit, finite difference method on non-uniform grids. We use a special non-uniform mesh in order to improve the numerical accuracy of the classical discrete fractional formula for the Caputo derivative. The stability and the convergence of the method are discussed. The error estimates established for a non-uniform grid and a uniform one are reported, to support the theoretical results. Numerical experiments are carried out to demonstrate the effectiveness of the method. View Full-Text
Keywords: time-fractional advection–diffusion–reaction equation; Caputo fractional derivative; implicit finite difference method; non-uniform grid; stability; convergence time-fractional advection–diffusion–reaction equation; Caputo fractional derivative; implicit finite difference method; non-uniform grid; stability; convergence
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Fazio, R.; Jannelli, A.; Agreste, S. A Finite Difference Method on Non-Uniform Meshes for Time-Fractional Advection–Diffusion Equations with a Source Term. Appl. Sci. 2018, 8, 960.

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