Numerical Solution to the Time-Fractional Burgers-Huxley Equation Involving the Mittag-Leffler Function

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255146" target="_blank" >RIV/61989100:27740/24:10255146 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2227-7390/12/13/2137" target="_blank" >https://www.mdpi.com/2227-7390/12/13/2137</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math12132137" target="_blank" >10.3390/math12132137</a>

Result language

angličtina

Original language name

Numerical Solution to the Time-Fractional Burgers-Huxley Equation Involving the Mittag-Leffler Function

Original language description

Fractional differential equations play a significant role in various scientific and engineering disciplines, offering a more sophisticated framework for modeling complex behaviors and phenomena that involve multiple independent variables and non-integer-order derivatives. In the current research, an effective cubic B-spline collocation method is used to obtain the numerical solution of the nonlinear inhomogeneous time-fractional Burgers-Huxley equation. It is implemented with the help of a theta-weighted scheme to solve the proposed problem. The spatial derivative is interpolated using cubic B-spline functions, whereas the temporal derivative is discretized by the Atangana-Baleanu operator and finite difference scheme. The proposed approach is stable across each temporal direction as well as second-order convergent. The study investigates the convergence order, error norms, and graphical visualization of the solution for various values of the non-integer parameter. The efficacy of the technique is assessed by implementing it on three test examples and we find that it is more efficient than some existing methods in the literature. To our knowledge, no prior application of this approach has been made for the numerical solution of the given problem, making it a first in this regard.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10100 - Mathematics

Project

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Continuities

O - Projekt operacniho programu

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Volume of the periodical

12

Issue of the periodical within the volume

13

Country of publishing house

CH - SWITZERLAND

Number of pages

22

Pages from-to

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UT code for WoS article

001267998000001

EID of the result in the Scopus database

2-s2.0-85198428834