Related papers: Exponential integrability properties of numerical …
We consider a linear partial integro-differential equation that arises in the modeling of various physical and biological processes. We study the problem in a spatial periodic domain. We analyze numerical stability and numerical convergence…
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…
Moist thermodynamics is a fundamental driver of atmospheric dynamics across all scales, making accurate modeling of these processes essential for reliable weather forecasts and climate change projections. However, atmospheric models often…
In this paper we study structure-preserving numerical methods for low Mach number barotropic Euler equations. Besides their asymptotic preserving properties that are crucial in order to obtain uniformly consistent and stable approximations…
A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…
We introduce a semi-implicit Euler-Maruyama approximation which preservers the non-colliding property for some class of non-colliding particle systems such as Dyson Brownian motions, Dyson-Ornstein-Uhlenbeck processes and Brownian particles…
Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators are considered. Under some regularity condition assumed for the solution, the rate of convergence of implicit Euler approximations is…
We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially…
In the present work, we delve into further study of numerical approximations of SDEs with non-globally monotone coefficients. We design and analyze a new family of stopped increment-tamed time discretization schemes of Euler, Milstein and…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We show that the probability of the exceptional set decays exponentially for a broad class of randomized algorithms approximating solutions of ODEs, admitting a certain error decomposition. This class includes randomized explicit and…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
In this paper we study time semi-discrete approximations of a class of exponentially stable infinite dimensional systems with unbounded feedbacks. It has recently been proved that for time semi-discrete systems, due to high frequency…
In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally H\"older continuous. We first…
Exponential integrators are explicit methods for solving ordinary differential equations that treat linear behaviour exactly. The stiff-order conditions for exponential integrators derived in a Banach space framework by Hochbruck and…
We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by obtained by computing a directional derivative of the weak…
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local…
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…