相关论文: A numerical test of differential equations for one…

This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…

The problem of existence of solutions to nabla differential equations and nabla differential inclusions on time scales is considered. Under a special form of the set-valued constraint map, sufficient conditions for the existence of at least…

Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…

We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…

So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…

Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…

We introduce a system of two linearly coupled discrete nonlinear Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC).…

Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…

A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several…

We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…

A class of two-dimensional linear differential systems is considered. The box-counting dimension of the graphs of solution curves is calculated. Criteria to obtain the box-counting dimension of spirals are also established.

We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…

Multiple sets of synthetic spectra of OB-binary stars are used to test the suitability of disentangling for deriving accurate spectroscopic orbits. Given a set of spectra with broad phase coverage and sufficient total integration time…

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

This paper focuses on the construction and analysis of explicit numerical methods of high dimensional stochastic nonlinear Schrodinger equations (SNLSEs). We first prove that the classical explicit numerical methods are unstable and suffer…

The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between…

This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…