Shifted Second-Kind Chebyshev Spectral Collocation-Based Technique‎ for Time-Fractional KdV-Burgers' Equation

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Atta Ahmed Gamal; Hassan Youssri Youssri

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Journal Paper

Paper Information

Journal: Iranian Journal of Mathematical Chemistry Year:2023 | Volume:14 | Issue:4 Page(s): 207-224

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Information Journal Paper

Title

Shifted Second-Kind Chebyshev Spectral Collocation-Based Technique‎ for Time-Fractional KdV-Burgers' Equation

Author(s)

Atta Ahmed Gamal | Hassan Youssri Youssri | Issue Writer Certificate

Keywords

Time-fractional KdV-Burgers' equation

Chebyshev polynomials

Collocation method

Convergence analysis

Abstract

‎The main goal of this research work is to provide a numerical technique based on choosing a set of basis functions for handling the third-order time-fractional Korteweg–De Vries Burgers' equation‎. ‎The trial functions are selected for the shifted second-kind Chebyshev polynomials (S2KCPs) compatible with the problem's governing initial and boundary conditions‎. ‎The spectral tau method transforms the equation and its underlying conditions into a nonlinear system of algebraic equations that can be efficiently numerically inverted with the standard Newton's iterative procedures after the approximate solutions have been expressed as a double expansion of the two chosen basis functions‎. ‎The truncation error is estimated‎. ‎Various numerical examples are displayed together with comparisons to other approaches in the literature to show the applicability and accuracy of the provided methodology‎. ‎Different numerical models are displayed and compared to other methods in the literature‎.

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