Spectral Collocation Method Based Upon Special Functions for Fractional Partial Differential Equations

Authored by: H. M. Srivastava , Khaled M. Saad , M. M. Khader , Harendra Singh

Handbook of Fractional Calculus for Engineering and Science

Print publication date:  February  2022
Online publication date:  February  2022

Print ISBN: 9781032047799
eBook ISBN: 9781003263517
Adobe ISBN:


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The main objective of this chapter is to present a systematic study of the spectral collocation models of fractional differential equations with the help of such special functions as the Chebyshev polynomials and the Legendre polynomials. The basic idea is to convert the models to involve a set of ordinary differential equations which are then solved using known methods such as the finite difference method. The Newton–Raphson method (NRM) is used to find the numerical solutions for a set of nonlinear algebraic equations. These results are verified in the classical case by comparison with an exact solution. For the non-integer case, the accuracy of the solution is verified by computing the residual error function (REF). In all cases, the results are found to be fairly accurate, and in all calculations the software program Mathematica is used.

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