Related papers: Classification of $n-$th order linear ODEs up to p…
The Carath\'eodory form of the calculus of variations belongs to the class of Lepage equivalents of first-order Lagrangians in field theory. Here, this equivalent is generalized for second- and higher-order Lagrangians by means of intrisic…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
This paper deals with the time evolution in the matter era of perturbations in Friedman-Lemaitre models with arbitrary density parameter $\Omega$, with either a zero cosmological constant, $\Lambda = 0$, or with a non-zero cosmological…
The Numerov method for linear second-order differential equations is generalized to include equations containing a first derivative term. The method presented has the same degree of accuracy as the ordinary Numerov sixth-order method. A…
We study gradient-based optimization methods obtained by directly discretizing a second-order ordinary differential equation (ODE) related to the continuous limit of Nesterov's accelerated gradient method. When the function is smooth…
In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought of as stratifications of thin Schubert cells into unions of…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
We find the group of equivalence transformations for equations of the form $y''= A(x)y' + F(y),$ where $A$ and $F$ are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method…
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…
A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional…
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems. In this way we develop an approach to a class of fourth order elliptic partial differential equations using the idea of splitting into…
We solve the local equivalence problem for second order (smooth or analytic) ordinary differential equations. We do so by presenting a {\em complete convergent normal form} for this class of ODEs. The normal form is optimal in the sense…
Working to lowest non-trivial order in fermions, we consider the four-derivative order corrected Lagrangian and supersymmetry transformations of the Euclidean Bagger-Lambert-Gustavsson theory. By demonstrating supersymmetric invariance of…
We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence…
In this paper, we present new techniques for solving a large variety of partial differential equations. The proposed method reduces the PDEs to first order differential equations known as classical equations such as Bernoulli, Ricatti and…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman…
A theory of local convexity for a second order differential equation (SODE) on a Lie algebroid is developed. The particular case when the SODE is homogeneous quadratic is extensively discussed.
This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection…
In this article we consider a linearized Calder\'on problem for polyharmonic operators of order $2m\ (m\ge 2)$ in the spirit of Calder\'on's original work [Cal80]. We give a uniqueness result for determining coefficients of order $\leq…