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

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt

2 Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

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.

Keywords

Main Subjects


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