Abstract This paper studies the boundary value problem for a fourth-order difference equation with three quasidifferences. The new existence criterion of at least one solution to issues considered is obtained using theory variational methods. main result illustrated in some examples.

In this paper, we obtain a fourth-order convergence method to solve systems of nonlinear equations. This method is based on a quadrature formulae. A general error analysis providing the fourth order of convergence is given. Numerical examples show the fourth-order convergence. This method does not use the second-order Fréchet derivative. 2006 Elsevier Inc. All rights reserved.

In this paper, by combining a new maximum principle of fourth-order equations with the theory of eigenline problems, we develop a monotone method in the presence of lower and upper solutions for some fourth-order ordinary differential equation boundary value problem. Our results indicate there is a relation between the existence of solutions of nonlinear fourth-order equation and the first eige...

Multiple permanent-wave trains in nonlinear systems are constructed by the asymptotic tailmatching method. Under some general assumptions, simple criteria for the construction are presented. Applications to fourth-order systems and coupled nonlinear Schrödinger equations are discussed.

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

Nonlinear dynamics of wave packets in two-dimensional parity-time-symmetric optical lattices near the phase transition point are analytically studied. A fourth-order equation is derived for the envelope of these wave packets. A pyramid diffraction pattern is demonstrated in both the linear and nonlinear regimes. Blow-up is also possible in the nonlinear regime for both focusing and defocusing n...

This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...