相关论文: Weak error expansion of the implicit Euler scheme
We show expansion \textit{\`a la Talay-Tubaro} of a stopped numerical scheme for the Langevin process in the case of a singular potential. In order to achieve this, we provide estimates on the associated semi-group of the process. The class…
We propose and analyze a variation of the Euler scheme for state constrained ordinary differential inclusions under weak assumptions on the right-hand side and the state constraints. Convergence results are given for the space-continuous…
According to Talay and Tubaro \cite{talay_expansion_1990}, the weak error between the solution to a stochastic differential equation with smooth coefficients and its Euler-Maruyama scheme can be expanded in powers of the time-step. In the…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
In the paper, we improve our earlier results concerning the existence, uniqueness and differentiability of a global implicit function. Some application to a Cauchy problem for an integro-differential Volterra system of nonconvolution type,…
We extend the theory of Euler integration from the class of constructible functions to that of "tame" real-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it…
In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Ku\v{c}era (JCP 2007) as well as the class of RS-IMEX schemes. The implicit part is based on a Jacobian matrix which is…
We prove an extension theorem for local solutions of the 3d incompressible Euler equations. More precisely, we show that if a smooth vector field satisfies the Euler equations in a spacetime region $\Omega\times(0,T)$, one can choose an…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
We discuss the (twisted) weak positivity theorem. We also treat some applications.
It is known from the monograph [1, Chapter 5] that the weak convergence analysis of numerical schemes for stochastic Maxwell equations is an unsolved problem. This paper aims to fill the gap by establishing the long-time weak convergence…
In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates of time-delay systems. An iterative…
In this paper, we introduce an efficient backpropagation scheme for non-constrained implicit functions. These functions are parametrized by a set of learnable weights and may optionally depend on some input; making them perfectly suitable…
We consider numerical approximations of stochastic Langevin equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a…
The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and…
We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a…
The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
We prove a weak-type estimate for a class of operators extending some of the almost orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.
We give some extensions of Mercer's theorem to continuous Carleman kernels inducing unbounded integral operators.