Related papers: Newton's Method Applied to Nonlinear Boundary Valu…
An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions…
A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
We consider the solution of variational equations on manifolds by Newton's method. These problems can be expressed as root finding problems for mappings from infinite dimensional manifolds into dual vector bundles. We derive the…
It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to solve nonlinear elliptic partial differential equations…
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear differential equations. It allows one to express exact solutions…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
We extend the ultraspherical spectral method to solving nonlinear ODE boundary value problems. We propose to use the inexact Newton-GMRES framework for which an effective preconditioner can be constructed and a fast Jacobian-vector…
A monotone iterative method is proposed to solve nonlinear discrete boundary value problems with the support of upper and lower solutions. We establish some new existence results. Under some sufficient conditions, we establish maximum…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-\Delta u + u = 0$ in $\Omega$ with $\frac{\partial u}{\partial…
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is established based on a proposed Coiflet based approximation scheme…
A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using seventh degree B-Spline function. Formulation is based on particular terms of order of seventh order…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…