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Research Article | Open Access

Efficient time second-order SCQ formula combined with a mixed element method for a nonlinear time fractional wave model

Yining Yang1, Yang Liu1( ), Cao Wen1, Hong Li1, Jinfeng Wang2( )
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China
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Abstract

In this article, a kind of nonlinear wave model with the Caputo fractional derivative is solved by an efficient algorithm, which is formulated by combining a time second-order shifted convolution quadrature (SCQ) formula in time and a mixed element method in space. The stability of numerical scheme is derived, and an optimal error result for unknown functions which include an original function and two auxiliary functions are proven. Further, the numerical tests are conducted to confirm the theoretical results.

Keywords

nonlinear time fractional wave modelsecond-order SCQ formulamixed finite element methodstabilityoptimal error estimate

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Electronic Research Archive
Volume 30 Issue 2,
February 2022
Pages 440-458
DOI: 10.3934/era.2022023

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Cite this article:
Yang Y, Liu Y, Wen C, et al. Efficient time second-order SCQ formula combined with a mixed element method for a nonlinear time fractional wave model. Electronic Research Archive, 2022, 30(2): 440-458. https://doi.org/10.3934/era.2022023

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Received: 18 December 2021
Revised: 18 January 2022
Accepted: 20 January 2022
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)