<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the present paper, a numerical scheme is discussed to solve one-dimensional nonlinear diffusion equation of fractional order in which collocation is performed using the Lucas operational matrix. Since the spectral collocation method is used in the proposed method, therefore the residual, initial and boundary conditions of the presented problem are collocated at fixed collocation points. The result is a system of nonlinear equations that can be solved by using Newton’s method. Through error analysis and application to some existing problems, the accuracy of the method is confirmed. The obtained results are presented in tabular forms, which clearly show the higher accuracy of the proposed method. The variations of the solute profile of the proposed model are shown graphically due to the presence or absence of advection and reaction terms for different particular cases.</p>
</abstract>

In the present paper, a numerical scheme is discussed to solve one-dimensional nonlinear diffusion equation of fractional order in which collocation is performed using the Lucas operational matrix. Since the spectral collocation method is used in the proposed method, therefore the residual, initial and boundary conditions of the presented problem are collocated at fixed collocation points. The result is a system of nonlinear equations that can be solved by using Newton’s method. Through error analysis and application to some existing problems, the accuracy of the method is confirmed. The obtained results are presented in tabular forms, which clearly show the higher accuracy of the proposed method. The variations of the solute profile of the proposed model are shown graphically due to the presence or absence of advection and reaction terms for different particular cases.

Operational matrix method to solve nonlinear reaction-advection-diffusion equation in fractional order system

Ovidius University of Constanta Bd. Mamaia 124

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In the present paper, a numerical scheme is discussed to solve one-dimensional nonlinear diffusion equation of fractional order in which collocation is...

Operational matrix method to solve nonlinear reaction-advection-diffusion equation in fractional order system

Published Online: Oct 08, 2022

Page range: 97 - 116

Received: Dec 30, 2021

Accepted: Mar 25, 2022

DOI: https://doi.org/10.2478/auom-2022-0036

Keywords
Lucas polynomial, operational matrix, spectral collocation method, nonlinear diffusion equation, error bound

© 2022 E-M. Craciun et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Operational matrix method to solve nonlinear reaction-advection-diffusion equation in fractional order system

Published Online: Oct 08, 2022

Page range: 97 - 116

Received: Dec 30, 2021

Accepted: Mar 25, 2022

DOI: https://doi.org/10.2478/auom-2022-0036

KeywordsLucas polynomial, operational matrix, spectral collocation method, nonlinear diffusion equation, error bound

© 2022 E-M. Craciun et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Lucas polynomial, operational matrix, spectral collocation method, nonlinear diffusion equation, error bound