Sentence examples for some nonlinear equations from inspiring English sources

The goal of this paper is to solve problem (1) which is more general and includes some nonlinear equations, such as boundary value problems [12].

One of the motivations for the renewed interest in the area has been Stević's method/idea for transforming some nonlinear equations into solvable linear ones (see, for example, [11, 13, 19, 20] and numerous related references therein).

In this paper, it is attempted to obtain some nonlinear equations between the results achieved from Chung and Lau's investigation (Chung and Lau 1999) by means of the artificial neural networks (ANNs).

Based on the mass, momentum and energy conservation, a mathematical model is built, which consists of some simultaneous nonlinear equations.

In this case, some of these nonlinear equations can be solved by numerical approaches, while some others are solvable using various analytical methods such as Perturbation method (PM) (Bhatti and Lu 2017), Collocation method (CM) (Rahimi et al. 2017; Atouei et al. 2015), Homotopy perturbation method (HPM), and Variational iteration method (VIM).

In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed.

Numerical assessments are made which justify the theoretical results: in particular, some systems of nonlinear equations associated with the numerical approximation of partial differential equations (PDEs) and ordinary differential equations (ODEs) are built up and solved.

They have the positive features of the Dai-Kou type methods for problem (2), they can be used to solve the nonlinear optimization (2) only requiring gradient information, and they can be used to solve some systems of nonlinear equations, such as those arising in boundary value problems and others.

Some pioneering works for nonlinear equations were initiated by Maday and Quarteroni [24] for steady-state spectral solutions.

This method is one of the strong and effect method for solving nonlinear problems and is investigated and developed by some authors to solve nonlinear equations arising in engineering problems.

The rest of the paper is structured as follows: in "Description of methods" we give brief descriptions of extended F-expansion and projective Riccati equation methods; in "Traveling wave reduction of some nonlinear evolution equations", a few NLEEs of physical interest are transformed into elliptic-like equations.