Leap-frog method for stochastic functional wave equations

Abstract

We perform a time-space discretisation, known as the leapfrog method, for nonlinear stochastic functional wave equations driven by multiplicative time-space white noise. To prove its stability we apply Cairoli's maximal inequalities for two-parameter martingales and provide a lemma for estimating solutions to a class of stochastic wave equations and a Gronwall-type inequality over cones. The method converges in L 2 at a rate of O(√ h), where h is a time-space step size.

Insight into Tryptophan-Dependent Interaction Mechanisms between Peptides and Anthocyanins for Stability Enhancement

“…To ensure the stability of the system, the prebalance processes were performed: the combination of energy minimization, NVT (constant number of particles, volume, and temperature), and NPT (constant number of particles, pressure, and temperatures) . The algorithm, steepest descent minimization, was applied to the energy minimization process, and the leapfrog integrator was used for both NVT and NPT. The pre-equilibrium steps were aimed to render the system sustain a relatively stable condition with a constant pressure (1 atm) and temperature (300 K) before the MD formal process …”

Newton's method for stochastic semilinear wave equations driven by multiplicative time‐space noise

“…A multiplicative noise case of SWE is treated in [20,31] (leap-frog scheme), [27] (method of lines) and [1,3] (fully discrete scheme), [4,23] (optimal weak convergence rates).…”