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

Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion... AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analele Universitatii "Ovidius" Constanta - Seria Matematica de Gruyter

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

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Publisher
de Gruyter
Copyright
© 2021 Manpal Singh et al., published by Sciendo
eISSN
1844-0835
DOI
10.2478/auom-2021-0027
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Analele Universitatii "Ovidius" Constanta - Seria Matematicade Gruyter

Published: Jun 1, 2021

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

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