Bernstein Operational Matrix with Error Analysis for Solving High Order Delay Differential Equations

Abstract

In this paper, we propose a numerical method based on Bernstein polynomials and their operational matrices for solving both linear and non-linear delay differential equations (DDEs). The Bernstein operational matrices for differentiation and delay functions are introduced. The aim is to reduce the DDEs to a set of algebraic equations. Moreover If the exact solution is polynomial, then the exact solution set will be obtained. Even the exact solution is unknown, an upper bound based on the regularity of the exact solution will be obtained. By using the residual correction procedure and the error analysis of the four- and five-order Runge–Kutta method (RK45) the absolute errors may be estimated and the approximate solution can be corrected. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results. © 2016, Springer India Pvt. Ltd.