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

Yining Yang; Yang Liu; Cao Wen; Hong Li; Jinfeng Wang; Yining Yang; Yang Liu; Cao Wen; Hong Li; Jinfeng Wang

doi:10.3934/era.2022023

Electronic Research Archive

2022, Volume 30, Issue 2: 440-458. doi: 10.3934/era.2022023

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

Yining Yang ¹,
Yang Liu ^{1
,
,},
Cao Wen ¹,
Hong Li ¹,
Jinfeng Wang ^{2
,
,}

1.
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
2.
School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China

Received: 18 December 2021 Revised: 18 January 2022 Accepted: 20 January 2022 Published: 24 January 2022

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.
- nonlinear time fractional wave model,
- second-order SCQ formula,
- mixed finite element method,
- stability,
- optimal error estimate
Citation: Yining Yang, Yang Liu, Cao Wen, Hong Li, Jinfeng Wang. Efficient time second-order SCQ formula combined with a mixed element method for a nonlinear time fractional wave model[J]. Electronic Research Archive, 2022, 30(2): 440-458. doi: 10.3934/era.2022023

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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.

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