Open AccessEfficient time second-order SCQ formula combined with a mixed element method for a nonlinear time fractional wave model
Author(s) -
Yining Yang,
AUTHOR_ID,
Yang Liu,
Wen Cao,
Hong Li,
Jinfeng Wang,
AUTHOR_ID
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022023
Subject(s) - quadrature (astronomy) , mathematics , nonlinear system , fractional calculus , convolution (computer science) , stability (learning theory) , space time , function (biology) , element (criminal law) , mathematical analysis , order (exchange) , computer science , physics , artificial neural network , finance , quantum mechanics , machine learning , evolutionary biology , optics , economics , biology , chemical engineering , law , political science , engineering
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.