Author:
Mahdi Amna M.,AL-Jawary Majeed A.,Mustafa Turkyilmazoglu
Abstract
The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very good agreement. In addition, the convergence of the proposed approximate methods is given based on one of the Banach fixed point theorem results.
Publisher
College of Education for Pure Science (Ibn Al-Haitham)
Reference31 articles.
1. Murphy, G.M. Ordinary Differential Equations and Their Solutions; Dover Publications, Inc., New York, 1960.
2. Boyce, W.E.; DiPrima, R.C. Elementary differential equations and boundary value problems, Ed.;9th ed. 2009; John Wiley & Sons, Inc., United States of America, 2009; ISBN 9780470383346.
3. Operational matrices of Bernstein polynomials and their applications
4. A computational method for solving a class of singular boundary value problems arising in science and engineering
5. Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow equations