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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Svazek periodika

12

Číslo periodika v rámci svazku

13

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

22

Strana od-do

—

Kód UT WoS článku

001267998000001

EID výsledku v databázi Scopus

2-s2.0-85198428834