Higher order graded mesh scheme for time fractional differential equations

2022/01/11 by Gande Naga Raju, Raju, Gande Naga, Harshita Madduri +1
Mathematics · #65L05 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2201.03766

openalex publication_date 2022/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time fractional partial differential equations (TFPDE). The proposed approximation for C-F derivative tackles the singularity at origin effectively and is easily applicable to diverse problems. The stability analysis and truncation error bounds of the proposed scheme are discussed, along with this, analyzed the required regularity of the solution. Few numerical examples are presented to support the theory.

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