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

• Autorzy: Hadhoud Adel R. , Alaal Faisal E. Abd , Abdelaziz Ayman A. , Radwan Taha

Identyfikatory

DOI

10.1515/dema-2021-0040

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

generalized time-fractional Huxley-Burgers’ equation; mean value theorem; cubic B-splines; collocation method; stability analysis

PL

równanie Burgersa; twierdzenie o wartości średniej; krzywa B-sklejana; metoda kolokacji; analiza stateczności

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 436--451
• Opis fizyczny: Bibliogr. 29 poz., rys., tab.

Twórcy

autor

Hadhoud Adel R.

• Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-kom, Egyp

autor

Alaal Faisal E. Abd

• Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt

autor

Abdelaziz Ayman A.

• Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt

autor

Radwan Taha

• Department of Mathematics, College of Science and Arts in Ar-Rass, Qassim University, Ar-Rass, Kingdom of Saudi Arabia
• Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said, Egypt

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).