Computational methods for solving nonlinear ordinary differential equations arising in engineering and applied sciences

In this paper, the computational method (CM) based on standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel methods have developed study by orthogonal base functions, namely Hermite, Legendre, Bernstein polynomials. The problem is successfully converted into a algebraic system of equations, which are then solved Mathematica®12. (D-CMs) three applications involving well-known problems: Darcy-Brinkman-Forchheimer equation, Blasius Falkner-Skan comparison between presented. addition, maximum error remainder () computed demonstrate accuracy proposed methods. results persuasively prove that CM D-CMs reliable accurate obtaining approximate solutions problems, with obvious superiority for than CM.