In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met

In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

What distinguishes the athlete in dealing with all stimuli is the ability to understand the cognitive rules through which he acts and directs behavior through thinking and regular planning methods in dealing with the environment in a realistic manner, and this comes through techniques and means based on modernity in obtaining information that makes the athlete arrange in His memory is the programs that are the most important crutch for relying on when he asks for them in applying and executing the skill assignment. One of the enhancers of awareness of variables is the ability of coaches to provide openness in modern ideas to find solutions, through which the player can sense and interpret events and produce outputs for quick and successful