Related papers: Conservative methods for stochastic differential e…
We develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that…
This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…
In order to approximate solutions of stochastic partial differential equations (SPDEs) that do not possess commutative noise, one has to simulate the involved iterated stochastic integrals. Recently, two approximation methods for iterated…
In this paper, we established the Freidlin-Wentzell type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the…
We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale. Compared to the deterministic case and as far as we work in $L^2$, the…
This paper investigates the mean-square exponential stability of neutral stochastic differential delay equations (NSDDEs) with Markovian switching. The analysis addresses the complexities arising from the interaction between the neutral…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…
We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of $\mathcal L^2$-convergence of the truncated SD method and showed…
Numerical analysis of conserved field dynamics has been generally performed with pseudo spectral methods. Finite differences integration, the common procedure for non-conserved field dynamics, indeed struggles to implement a conservative…
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
Mean square exponential stability of $\theta$-EM and modified truncated Euler-Maruyama (MTEM) methods for stochastic differential delay equations (SDDEs) are investigated in this paper. We present new criterion of mean square exponential…
For the stochastic differential equation (SDE) which has piecewise continuous arguments (PCAs), is driven by multiplicative noises and its drift coefficients are dissipative, we show that the solution at integer time is a Markov chain and…
We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension we numerically simulate singular solutions (peakons)…