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

<p>In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known.</p>
</abstract>

In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known.

Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method

Faculty of Mechanical, Industrial and Maritime Engineering

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with...

Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method

Published Online: Jul 08, 2021

Page range: 211 - 230

Received: Oct 30, 2020

Accepted: Nov 30, 2020

DOI: https://doi.org/10.2478/auom-2021-0027

Keywords
Caputo fractional derivative, Operational matrix, Lucas polynomial, Collocation method, Reaction-advection-diffusion equation

© 2021 Manpal Singh et al., published by Sciendo

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

Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method

Published Online: Jul 08, 2021

Page range: 211 - 230

Received: Oct 30, 2020

Accepted: Nov 30, 2020

DOI: https://doi.org/10.2478/auom-2021-0027

KeywordsCaputo fractional derivative, Operational matrix, Lucas polynomial, Collocation method, Reaction-advection-diffusion equation

© 2021 Manpal Singh et al., published by Sciendo

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

Keywords
Caputo fractional derivative, Operational matrix, Lucas polynomial, Collocation method, Reaction-advection-diffusion equation