Related papers: On the Convergence of the Variational Iteration Me…
Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.
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 consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…
We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative).…
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
We formulate the initial value problem for causal variational principles in the continuous setting on a compact metric space. The existence and uniqueness of solutions is analyzed. The results are illustrated by simple examples.
In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions of a first-order ordinary differential equation with…
We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed…
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under…
In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We prove a result on the convex dependence of solutions of ordinary differential equations on an ordered finite-dimensional real vector space with respect to the initial data.
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…
We show that a recent application of homotopy perturbation method to a class of ordinary differential equations yields either useless or wrong results.