相关论文: Remark on Periodic Solutions of Non Linear Oscilla…

Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…

In this paper we consider a class of nonlinear wave equation with $x$-dependent coefficients and prove existence of families of time-periodic solutions under the general boundary conditions. Such a model arises from the forced vibrations of…

In this work, we propose a parallel-in-time solver for linear and nonlinear ordinary differential equations. The approach is based on an efficient multilevel solver of the Schur complement related to a multilevel time partition. For linear…

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…

It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…

Nonoscillatory second order differential equations always admit ``special'', principal solutions. For a certain type of oscillatory equation principal pairs of solutions were introduced by \'A. Elbert, F. Neuman and J. Vosmansk\'y, {\em…

In this paper we discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators . We show that the main equations are inconsistent and for that reason the results may be of scarce utility.

We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…

This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…

A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…

In the paper we analyse the exact solutions to scalar PDEs obtained thanks to summable Taylor series provided by Adomian's decomposition method. We propose the modification of the method which makes the calculations of Taylor coefficients…

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 study, we examine the asymptotic behavior of solutions to nonlinear Schr\"{o}dinger equations with time-dependent harmonic oscillators and prove the time-decay property of solutions in the case of a long range power type…

In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to…

We discuss a weighted variational integral approach for nonlocal linear diffusion models with forcing term, providing a selection principle for solutions of elliptic in time regularizations.

The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…

In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…

We present a general method to obtain asymptotic power series for three kinds of sequences. And we give recurrence relations for determining the coefficients of asymptotic power series for these sequences. As applications, we show how these…

Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…

In this article we present solutions of certain polynomial equations in periodic nested radicals. We also present a new way to solve the general tetranomial equation with new functions. As application of these new functions we solve the…