Long time numerical behaviors of fractional pantograph equations

Dongfang Li and Chengjian Zhang

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 172, issue C, 244-257

Abstract: This paper is concerned with long time numerical behaviors of nonlinear fractional pantograph equations. The L1 method with the linear interpolation procedure is applied to solve these nonlinear problems. It is proved that the proposed numerical scheme can inherit the long time behavior of the underlying problems without any stepsize restrictions. After that, the fast evaluation is presented to speed up the calculation of the Caputo fractional derivative. Numerical examples are shown to confirm the theoretical results. Besides, several counter-examples are also given to show that not all the numerical methods can inherit the long time behavior of the underlying problems.

Keywords: Long time behavior; Stability; Fractional pantograph equations; Fast algorithm (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:172:y:2020:i:c:p:244-257

DOI: 10.1016/j.matcom.2019.12.004

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