Related papers: Development of numerical methods for nonlinear hyb…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…
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…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in \cite{cstv}, and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of…
This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H\"older continuous drifts and locally H\"older continuous diffusion coefficients. To handle with the superlinear terms in…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
Stochastic partial differential equations (SPDEs) have become a crucial ingredient in a number of models from economics and the natural sciences. Many SPDEs that appear in such applications include non-globally monotone nonlinearities.…
A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
In this paper, we investigate a class of stochastic impulsive fractional differential evolution equations with infinite delay in Banach space. Firstly sufficient conditions of the existence and uniqueness of the mild solution for this type…
In this article, we give a unified theory for constructing boundary layer expansions for dis-cretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…