Numerical analysis of linear and nonlinear time-fractional subdiffusion equations

Abstract

In this paper, a new type of the discrete fractional Gr{ö}nwall 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 Gr{ö}nwall inequality is also applied to prove the unconditional convergence of a semi-implicit Galerkin spectral method for a nonlinear time-fractional subdiffusion equation.

arXiv comment16 pages

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• A new difference scheme for the time fractional diffusion equation
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Cited by in corpus (1)

• Strong convergence rates of an exponential integrator and finite elements method for time-fractional SPDEs driven by Gaussian and non-Gaussian noises