相关论文: Integrating factors for second order ODEs

We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable $X$. This algorithm rests on the factorization $X=Y Y^T$, where the number of columns of Y fixes the rank of…

Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics. In this paper we undertake these problems and…

This note considers fairly general quasi-homogeneous systems of first-order nonlinear ODEs and homogeneous systems of second-order nonlinear ODEs that contain arbitrary functions of several arguments. It presents several exact solutions to…

We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the Gambier method that led to the equation that…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Nonconvex optimization problems are widespread in modern machine learning and data science. We introduce an extrapolation strategy into a class of preconditioned second-order convex splitting algorithms for nonconvex optimization problems.…

The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…

A method of finding general solutions of second-order nonlinear ordinary differential equations by extending the Prelle-Singer (PS) method is briefly discussed. We explore integrating factors, integrals of motion and the general solution…

We investigate and derive second solutions to linear homogeneous second-order difference equations using a variety of methods, in each case going beyond the purely formal solution and giving explicit expressions for the second solution. We…

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…

We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form \[ \exp(\int r \,…

We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…

We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.

We have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have established solid theoretical basis through a relation between the…

Here we present a method to find elementary first integrals of rational second order ordinary differential equations (SOODEs) based on a Darboux type procedure \cite{ManMac,firsTHEOps1,secondTHEOps1}. Apart from practical computational…

We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our…

In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…

This paper generalizes the results obtained in an earlier paper (math.OA/0003087) for finite factors to infinite but still semifinite factors. First we give a characterization of cyclic and separating vectors for infinite semifinite factors…

This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…

In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity…