Bernstein collocation method for solving nonlinear differential equations

Abstract

In this study, a collocation method based on Bernstein polynomials is developed for solution of the nonlinear ordinary differential equations with variable coefficients, under the mixed conditions. These equations are expressed as linear ordinary differential equations via quasilinearization method iteratively. By using the Bernstein collocation method, solutions of these linear equations are approximated. Combining the quasilinearization and the Bernstein collocation methods, the approximation solution of nonlinear differential equations is obtained. Moreover, some numerical solutions are given to illustrate the accuracy and implementation of the method.