Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions

[摘要] In this study, we present the Bernstein matrix method to solve the first order nonlinear ordinary differential equations with the mixed non-linear conditions. By using this method, we obtain the approximate solutions in form of the Bernstein polynomials [1,2,16,17]. The method reduces the problem to a system of the nonlinear algebraic equations by means of the required matrix relations of the solutions form. By solving this system, the approximate solution is obtained. Finally, the method will be illustrated on the examples.

[学科分类] 计算数学

[关键词] nonlinear ordinary differential equations;riccati equation;Bernstein polynomials;collocation points