Novel Approximate Solutions for Nonlinear Blasius Equations

Authors

Amna M. Mahdi Department of Mathematics, College of Education for Pure Sciences Ibn AL-Haitham, University of Baghdad, Baghdad, Iraq.
Majeed A. AL-Jawary Department of Mathematics, College of Education for Pure Sciences Ibn AL-Haitham, University of Baghdad, Baghdad, Iraq.
Mustafa Turkyilmazoglu Department of Mathematics, Hacettepe University, Ankara, Turkey. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.

DOI:

https://doi.org/10.30526/37.1.3292

Keywords:

Blasius equations; Bernstein polynomial; Legendre polynomial; Bernoulli polynomial; operational matrices.

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 4^th 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.

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