Related papers: Constructing discrete Painlev\'e equations: from E…
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…
The well known elliptic discrete Painlev\'e equation of Sakai is constructed by a standard translation on the $E_8^{(1)}$ lattice, given by nearest neighbor vectors. In this paper, we give a new elliptic discrete Painlev\'e equation…
Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of the equation that corresponds to the linear variational…
We investigate the problem of recovering coefficients in scalar nonlinear ordinary differential equations that can be exactly linearized. This contribution builds upon prior work by Lyakhov, Gerdt, and Michels, which focused on obtaining a…
We present a high-order spacetime numerical method for discretizing and solving linear initial-boundary value problems using wavelet-based techniques with user-prescribed error estimates. The spacetime wavelet discretization yields a system…
Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…
We develop the structure theory for transformations of weakly geometric rough paths of bounded $1 < p$-variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We…
We show that the discrete Kadomtsev-Petviashvili (KP) equation with sources obtained recently by the "source generalization" method can be incorporated into the squared eigenfunction symmetry extension procedure. Moreover, using the known…
For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher) symmetry of a system and a symmetry-invariant conservation…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…
Solving eigenvalue problems is crucially important for both classical and quantum applications. Many well-known numerical eigensolvers have been developed, including the QR and the power methods for classical computers, as well as the…
We study the dependence of recurrence coefficients in the three-term recurrence relation for orthogonal polynomials with a certain deformation of the $q$-Laguerre weight on the degree parameter $n$. We show that this dependence is described…
We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…
This article is the first one in a suite of three articles exploring connections between dynamical systems of St\"{a}ckel-type and of Painlev\'{e}- type. In this article we present a deformation of autonomous St\"{a}ckel-type systems to…
We investigate self-similar solutions of the extended discrete KP hierarchy. It is shown that corresponding ansatzes lead to purely discrete equations with dependence on some number of parameters together with equations governing…
In this note, we review the notion of Painlev\'e scheme of the sixth Painlev\'e equation from the viewpoint of accessible singular point and its local index in the Hirzebruch surface of degree two ${\Sigma_2}$. The key method is Painlev\'e…