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Some Second-Order σ Schemes Combined with an H1-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
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Mathematics 2020, 8(2), 187; https://doi.org/10.3390/math8020187
Received: 8 November 2019 / Revised: 26 January 2020 / Accepted: 28 January 2020 / Published: 4 February 2020
(This article belongs to the Section Mathematics and Computer Science)
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 σ scheme; interpolation approximation; H1-Galerkin mixed finite element method; nonlinear distributed-order sub-diffusion equation; stability; error estimates second-order σ scheme; interpolation approximation; H1-Galerkin mixed finite element method; nonlinear distributed-order sub-diffusion equation; stability; error estimates
MDPI and ACS Style

Hou, Y.; Wen, C.; Li, H.; Liu, Y.; Fang, Z.; Yang, Y. Some Second-Order σ Schemes Combined with an H1-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation. Mathematics 2020, 8, 187.

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