shifted second-kind chebyshev spectral collocation-based technique‎ for time-fractional kdv-burgers’ equation

‎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.