相关论文: Rigorous numerical computation of the Stokes multi…

The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness…

We introduce a new rigorous method, based on Borel summability and asymptotic constants of motion generalizing \cite{invent} and \cite{ode1}, to analyze singular behavior of nonlinear ODEs in a neighborhood of infinity and provide global…

A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.

For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…

In this paper we study analytic (linear or) nonlinear systems of ordinary differential equations, at an irregular singularity of rank one, under nonresonance conditions. It is shown that the formal asymptotic exponential series solutions…

This paper is a continuation of our previous work \cite{St} where we have studied the Stokes phenomenon for a particular family of equation \eqref{initial} with \eqref{form-0}-\eqref{npe} from a perturbative point of view. Here we focus on…

In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…

In this paper we present an arbitrary-order fully discrete Stokes complex on general polyhedral meshes. We enriche the fully discrete de Rham complex with the addition of a full gradient operator defined on vector fields and fitting into…

We investigate geometric aspects of co-equational parametric resurgence, by studying physical problems whose formal asymptotic solutions give rise to Borel transforms lying on an algebraic curve. This perspective allows us to elucidate…

A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…

Hyperasymptotics is an analytical method that incorporates exponentially small contributions into asymptotic approximations, thereby expanding their domain of validity, improving accuracy, and providing deeper insight into the underlying…

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 present a new open source implementation in the SageMath computer algebra system of algorithms for the numerical solution of linear ODEs with polynomial coefficients. Our code supports regular singular connection problems and provides…

This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…

Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a…

A precise description of the singularities of the Borel transform of solutions of a level-one linear differential system is deduced from a proof of the summable-resurgence of the solutions by the perturbative method of J. \'Ecalle. Then we…

The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…

In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…

In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to the Fast…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…