Some Second-Order ? Schemes Combined with an H 1 -Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation

Yaxin Hou, Cao Wen, Hong Li, Yang Liu, Zhichao Fang and Yining Yang
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Yaxin Hou: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Cao Wen: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Hong Li: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Yang Liu: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Zhichao Fang: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Yining Yang: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Mathematics, 2020, vol. 8, issue 2, 1-19

Abstract: In this article, some high-order time discrete schemes with an H 1 -Galerkin mixed finite element (MFE) method are studied to numerically solve a nonlinear distributed-order sub-diffusion model. Among the considered techniques, the interpolation approximation combined with second-order σ schemes in time is used to approximate the distributed order derivative. The stability and convergence of the scheme are discussed. Some numerical examples are provided to indicate the feasibility and efficiency of our schemes.

Keywords: second-order ? scheme; interpolation approximation; H 1 -Galerkin mixed finite element method; nonlinear distributed-order sub-diffusion equation; stability; error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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