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Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the…

In this paper, the symmetry group of a differential system of n quadratic homogeneous first order ODEs of n variables is studied. For this purpose, we consider the action of both point and contact transformations to signify the…

In this paper, we discuss the method of obtaining symmetries for second order nonhomogeneous neutral differential equations with variable coefficients. We use Taylor theorem for a function of several variables to obtain a Lie type…

The Obreshkov method is a single-step multi-derivative method used in the numerical solution of differential equations and has been used in recent years in efficient circuit simulation. It has been shown that it can be made of arbitrary…

A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called…

The paper studies the harmonic maps on a direction between a Riemannian space and a generalized Lagrange space. Also, it is proved there that the solutions of C^2 class of certain ODEs or PDEs are harmonic maps, in the sense of this paper.

In this paper we introduce an observer design framework for ordinary differential equation (ODE) systems based on various types of existing or even novel one-parameter symmetries (exact, asymptotic and variational) ending up with a certain…

Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers. These solvers are computationally expensive, requiring the use of tiny step sizes for numerical stability and…

This paper presents an algorithm for calculating an ensemble of solutions to natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction reliability.…

While not generally a conservation law, any symmetry of the equations of motion implies a useful reduction of any second-order equationto a first-order equation between invariants, whose solutions (first integrals) can then be integrated by…

A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…

Whereas Lie had linearized scalar second order ordinary differential equations (ODEs) by point transformations and later Chern had extended to the third order by using contact transformation, till recently no work had been done for higher…

The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…

We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…

This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and…

Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…

We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…

This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems…

This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems…

In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic…