Abstract We address a new numerical method based on class of machine learning methods, the so-called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for computation steady-state solutions construction (one-dimensional) bifurcation diagrams nonlinear partial differential equations (PDEs). For our illustrations, we considered two benchmark problems, namely (a) one-...

The solution of a nonlinear boundary value problem in ordinary differential equations the form $ L(x(t))+f(x(t)) = 0 can be obtained by solving associated system equations. In this paper, three-step iterative method with ninth order convergence is proposed to solve scheme kept free from second and higher Frechet derivatives make it computationally efficient. discretized produce which then solve...

in this paper‎, ‎we consider the following kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{r}^{3}}|nabla u|^{2}right)delta u+v(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$uin h^{1}(mathbb{r}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎the aim of this paper is to study the existence of positive ...

Solving nonlinear equations is a problem often needed to be dealt with in the practical engineering application. This paper discusses preconditioning methods based on Block Broyden method. It first introduces the Block Broyden method and preconditioning technique. Then it presents four different preconditioners for the Block Broyden method and discusses the implementation process. It also analy...

The present work deals with the construction of a high‐order efficient technique for solving one‐dimensional nonlinear Bratu‐type and Lane‐Emden‐type problems describing various physical, chemical biological phenomena in applied science engineering. Convergence analysis method is studied. Numerical experiments are carried out to demonstrate efficiency, accuracy performance proposed method. show...

Solving nonlinear equations is a problem that needs to be dealt with in the practical engineering application. This paper uses Block–Broyden method for solving large-scale nonlinear systems, and two preconditioners are applied for solving the underlying linear systems, including SSOR preconditioner as well as ASSOR method, which is based on SSOR. It discusses their implementation processes and ...