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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.
Analele Universitatii "Ovidius" Constanta - Seria Matematica – de Gruyter
Published: Jun 1, 2021
Keywords: Caputo fractional derivative; Operational matrix; Lucas polynomial; Collocation method; Reaction-advection-diffusion equation
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