相关论文: Factorization technique and isochronous condition …

The existence of a semiconjugate relation permits the transformation of a higher order difference equation on a group into an equivalent triangular system of two difference equations of lower orders. Introducing time-dependent form…

Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…

We design and analyse a new numerical method to solve ODE system based on the structural method. We compute approximations of solutions together with its derivatives up to order $K$ by solving an entire block corresponding to $R$ time…

We propose an alternative method to factorize an integer by using three harmonic oscillators. These oscillators are coupled together via specific Kerr nonlinear interactions. This method can be applied even if two harmonic oscillators are…

This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…

In the present time we observe a growing number of publications where the, so-called, flow equations are successfully used to diagonalize Hamiltonians by means of an appropriate unitary transformation. Here we discuss and compare the flow…

This paper studies the problem of state estimation for linear time-invariant descriptor systems in their most general form. The estimator is a system of ordinary differential equations (ODEs). We introduce the notion of partial causal…

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…

The Adomian decomposition method is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The aim of this paper is to apply Adomian decomposition method to obtain approximate solutions of nonlinear…

We study the problem of decomposition (non-commutative factorization) of linear ordinary differential operators near an irregular singular point. The solution (given in terms of the Newton diagram and the respective characteristic numbers)…

The method of factorization, based on the model of unstable particles with a smeared mass, is applied to the processes with an unstable particle in the intermediate state. It was shown, that in the framework of the method suggested, the…

We discuss a general method by which a higher order difference equation on a group is transformed into an equivalent triangular system of two difference equations of lower orders. This breakdown into lower order equations is based on the…

The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…

We present a semi-decision procedure to tackle first order differential equations, with Liouvillian functions in the solution (LFOODEs). As in the case of the Prelle-Singer procedure, this method is based on the knowledge of the integrating…

This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…

In this paper, we consider the initial value problem for some nonlinear second-order ODEs of Duffing type. We study the large time behavior of the solutions to this problem, from both the perspectives of mathematical and numerical analysis.…

We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…

A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…

In this study, a species-clustered ordinary differential equations (ODE) solver for chemical kinetics with large detailed mechanisms based on operator-splitting is presented. The ODE system is split into clusters of species by using graph…

To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…