A Finite Difference Method on Quasi-uniform Mesh for Time-Fractional Advection-Diffusion Equations with Source Term

2018/01/19 by Riccardo Fazio, Fazio, Riccardo, Alessandra Jannelli +1
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1801.07160

openalex publication_date 2018/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform grids. We use a special quasi-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 quasi-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.

Citations

• The random walk's guide to anomalous diffusion: a fractional dynamics approach

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