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Pseudospectral quadrature simulation technique for spatio-temporally parabolic multi-dimensional nonlinear fractional evolution equation

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Abstract

The aim of this paper, the author is to introduce the Jacobi pseudospectral quadrature simulation technique for the multi-dimensional nonlinear fractional evolution equation. We define Lagrange interpolants polynomial as a test function, which satisfies the Kronecker delta property at Jacobi-Gauss-Lobatto points. For this point, Jacobi polynomials are introduced and their functional grids of partial joining an item are determined. Utilizing the Jacobi derivatives matrices the given multi-dimensional nonlinear fractional evolution equations are reduced to a system of nonlinear algebraic equations, which will be solved using Newton’s Raphson method. The proposed strategy is set up in both directions to demonstrate the numerical solutions and to prove the theory of error estimates for the equations. The proficiency, precision, and legitimacy of the introduced strategy are exhibited by its application to three test models and compared with exact solutions and other existing methods. Besides, the proposed numerical method is reported to demonstrate the efficiency of our scheme. A comparison of the numerical and exact solutions is shown in figures and tables.

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Acknowledgements

The authors sincerely thank the reviewers for providing constructive comments for improvement of the manuscript. The first author thankfully acknowledges to the Ministry of Human Resource Development, India, for providing financial support for this research.

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  1. Centre for Advanced Data Science, VIT Chennai, Chennai, Tamil Nadu, 600127, India

    A. K. Mittal

  2. Department of Mathematics, SAS, VIT Chennai, Chennai, Tamil Nadu, 600127, India

    A. K. Mittal

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Mittal, A.K. Pseudospectral quadrature simulation technique for spatio-temporally parabolic multi-dimensional nonlinear fractional evolution equation. J Anal (2024). https://doi.org/10.1007/s41478-024-00750-3

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