A numerical approach for solving variable order differential equations using Bernstein polynomials

Abstract

In this study, a numerical technique is applied to investigate solutions of linear variable order differential equations(VODEs) in fluid mechanics. We investigate variable order(VO) in the Caputo sense. Our aim is to apply Bernstein polynomials(Bps) as the basis functions and operational matrices. We calculate two types of operational matrices of Bps. Using these operational matrices the main equation can be transformed into a system of algebraic equations, which must then be solved to get approximate solutions. Some examples are provided to indicate the accuracy of the presented method.