Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences

Nonlinear Engineering

Al-Jawary Majeed A.¹  Ibraheem Ghada H.¹ 

[1] Department of Mathematics, College of Education for Pure Sciences (Ibn AL-Haitham), University of Baghdad, Baghdad, Iraq;

关键词: nonlinear differential equations;    approximate solution;    bernstein polynomials;    chebyshev polynomials;    magnetohydrodynamic squeezing fluid;    jeffery-hamel flow;   

DOI  :  10.1515/nleng-2020-0012

来源: DOAJ

【 摘 要 】

In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using Mathematica® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To illustrate the accuracy and efficiency of the proposed methods, the maximum error remainder is calculated. The results shown that the proposed methods are accurate, reliable, time saving and effective. In addition, the approximate solutions are compared with the fourth order Runge-Kutta method (RK4) achieving good agreements.

【 授权许可】

Unknown