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arXiv · 2109.02798

L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term

Sudhakar Chaudhary·Pari J. Kundaliya
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Abstract

The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose a method for solving time fractional diffusion equation with nonlocal diffusion term. The proposed method comprises L1 scheme on graded mesh, finite element method and Newton's method. We discuss the well-posedness of the weak formulation at discrete level and derive \emph{a priori} error estimates for fully-discrete formulation in $L^2(Ω)$ and $H^1(Ω)$ norms. Finally, some numerical experiments are conducted to validate the theoretical findings.

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Sudhakar Chaudhary, Pari J. Kundaliya. 2022-01-07. L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term. https://arxiv.org/abs/2109.02798

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