%0 Journal Article
%T Shifted Second-Kind Chebyshev Spectral Collocation-Based Technique for Time-Fractional KdV-Burgers' Equation
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Atta, Ahmed Gamal
%A Hassan Youssri, Youssri
%D 2023
%\ 12/01/2023
%V 14
%N 4
%P 207-224
%! Shifted Second-Kind Chebyshev Spectral Collocation-Based Technique for Time-Fractional KdV-Burgers' Equation
%K Time-fractional KdV-Burgers' equation
%K Chebyshev polynomials
%K Collocation method
%K Convergence analysis
%R 10.22052/ijmc.2023.252824.1710
%X 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.
%U https://ijmc.kashanu.ac.ir/article_114102_4f98190a4c99d232347d42467073fe23.pdf