Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination-Reference-Cited by-同舟云学术

Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

Published:2021-01-01 Issue:1 Volume:54 Page:436-451
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Hadhoud Adel R.¹,Abd Alaal Faisal E.²,Abdelaziz Ayman A.²,Radwan Taha³⁴

Affiliation:

1. Department of Mathematics and Computer Science, Faculty of Science, Menoufia University , Shebin El-kom , Egypt

2. Department of Mathematics, Faculty of Science, Damanhour University , Damanhour , Egypt

3. Department of Mathematics, College of Science and Arts in Ar-Rass, Qassim University , Ar-Rass , Kingdom of Saudi Arabia

4. Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University , Port Said , Egypt

Abstract

Abstract In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2021-0040/pdf

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