Bernstein basis functions based algorithm for solving system of third order initial value problems

For obtaining numerical solutions of the system of ordinary differential equations (ODEs) of third order, a new numerical technique is proposed by using operational matrices of Bernstein polynomials. These operational matrices can be utilized to solve different problems of integral and differential equations. The System of third-order ODEs occur in various physical and engineering models. In this paper, an iterative algorithm is constructed by using operational matrices of Bernstein polynomials for solving the system of third order ODEs. The proposed technique provides a numerical solution by discretizing the system to a system of algebraic equations which can be solved directly. The method will be verified by using appropriate examples which are arising in Physics and some Engineering problems. The comparison of approximate and exact solution of the given examples is demonstrated with the help of tables and graphs. (C) 2020 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

Automated summary

A new numerical technique using operational matrices of Bernstein polynomials is proposed to obtain numerical solutions of third-order ordinary differential equations (ODEs). These operational matrices can be used for solving various problems in integral and differential equations. The method discretizes the system into algebraic equations for direct solution and is verified using examples from Physics and Engineering, demonstrating comparison between approximate and exact solutions through tables and graphs.