Related papers: Ordinary differential equations with point interac…
In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…
We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…
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…
The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…
We present a framework which enables the analysis of dynamic inverse problems for wave phenomena that are modeled through second-order hyperbolic PDEs. This includes well-posedness and regularity results for the forward operator in an…
This work deals with Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem. We first establish a Lipschitz stability result for this problem under a…
We are interested in the relative conditioning of the problem $y_0\mapsto \mathrm{e}^{tA}y_0$, i.e., the relative conditioning of the action of the matrix exponential $\mathrm{e}% ^{tA}$ on a vector with respect to perturbations of this…
Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…
We specialize Olver's and Rosenau's side condition heuristics for the determination of particular invariant sets of ordinary differential equations. It turns out that side conditions of so-called LaSalle type are of special interest.…
We observe that, up to conjugation, a majority of symmetric higher order ODEs (ordinary differential equations) and ODE systems have only fiber-preserving point symmetries. By exploiting Lie's classification of Lie algebras of vector…
By using Lie symmetry methods, we identify a class of second order nonlinear ordinary differential equations invariant under at least one dimensional subgroup of the symmetry group of the Ermakov-Pinney equation. In this context, nonlinear…
In this work, we establish a connection between the extended Prelle-Singer procedure with other widely used analytical methods to identify integrable systems in the case of $n^{th}$-order nonlinear ordinary differential equations (ODEs). By…
A new method of solving third-order ordinary complex differential equations (OCDEs) by generalizing Prelle-Singer. The idea which is a procedure for finding the solution for second-order differential equations in the real domain. We have…
Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…
This paper is concerned with the problem of existence of periodic solutions for perturbative Carath\'{e}odory differential equations. The main result provides sufficient conditions on the averaged equation that guarantee the existence of…