Numerical algorithm for time-fractional Sawada-Kotera equation and Ito equation with Bernstein polynomials

Abstract

The generalized KdV equation arises in many problems in mathematical physics. In this paper, an effective numerical method is proposed to solve two types of time-fractional generalized fifth-order KdV equations, the time-fractional Sawada-Kotera equation and Ito equation, the idea is to use Bernstein polynomials. Firstly, Bernstein basis polynomials are utilized to approximate unknown function and the error bound is given. Secondly, the representation of Bernstein basis polynomials are proposed to easily and quickly obtain the integer and fractional differential operator of unknown function, by which the studied equations can be displayed as the combination of operator matrices. Finally, comparison with Chebyshev wavelets method and the error data are presented to demonstrate the high accuracy and efficiency of Bernstein polynomials method for this kind of wave equations.