The Operational Matrices Methods for Solving Falkner-Skan Equations

Amna M. Mahdi; Majeed A. Al-Jawary

doi:10.24996/ijs.2022.63.12.36

Authors

Amna M. Mahdi partment of Mathematics, College of Education for Pure Sciences (Ibn AL-Haitham) / University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0001-7140-2144
Majeed A. Al-Jawary partment of Mathematics, College of Education for Pure Sciences (Ibn AL-Haitham) / University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0003-3967-0012

DOI:

https://doi.org/10.24996/ijs.2022.63.12.36

Keywords:

Falkner-Skan equation, Bernoulli polynomial, Legendre polynomial, operational matrix

Abstract

The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica^®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives a good agreement.