Numerical analysis of linear and nonlinear time-fractional subdiffusion equations

2019/01/21 by Yubo Yang, Yang, Yubo, Fanhai Zeng +1
Engineering · Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1901.06814

openalex publication_date 2019/01/21 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

In this paper, a new type of the discrete fractional Grönwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdiffusion equation. Based on the temporal-spatial error splitting argument technique, the discrete fractional Grönwall inequality is also applied to prove the unconditional convergence of a semi-implicit Galerkin spectral method for a nonlinear time-fractional subdiffusion equation.

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