Related papers: Monotone-iterative technique for an initial value …
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
In this paper, we consider the solvability of a class of nonlinear fourth order integro-differential equations with Navier boundary condition. We first deal with a corresponding linear problem and establish a maximum principle. Using the…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…
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…
In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes…
An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian…
The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
Various traditional numerical methods for solving initial value problems of differential equations often produce local solutions near the initial value point, despite the problems having larger interval solutions. Even current popular…
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by…