A numerical approach for solving variable order differential equations based on Bernstein polynomials

A numerical technique for solving a class of nonlinear variable order differential equations is introduced by using Bernstein Polynomials (BPs). Here, we apply the operational matrix of BPs. With this matrix, the main equation is transformed into a system of algebraic equations by expanding the solution as BPs with unknown coefficients. Then, by solving algebraic equations, the numerical solutions are obtained. The results of numerical examples indicate that the proposed method is computationally efficient.