Difference methods for time discretization of stochastic wave equation

by   Xing Liu, et al.

The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time discretization, whose the strong convergence order is smaller than 1 in the sense of mean-squared L^2-norm. Meanwhile, by modifying the low order method with trapezoidal rule, the convergence rate is improved at expenses of requiring some extra temporal regularity to the solution. The modified scheme has superlinear convergence rate under the mean-squared L^2-norm. Several numerical experiments are provided to confirm the theoretical error estimates.


page 1

page 2

page 3

page 4


Higher order approximation for stochastic wave equation

The infinitesimal generator (fractional Laplacian) of a process obtained...

High-accuracy time discretization of stochastic fractional diffusion equation

A high-accuracy time discretization is discussed to numerically solve th...

Strong approximation for fractional wave equation forced by fractional Brownian motion with Hurst parameter H∈(0,1/2)

We consider the time discretization of fractional stochastic wave equati...

Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping

The paper establishes the strong convergence rates of a spatio-temporal ...

Reducing Discretization Error in the Frank-Wolfe Method

The Frank-Wolfe algorithm is a popular method in structurally constraine...

Error estimate of the nonuniform L1 type formula for the time fractional diffusion-wave equation

In this paper, a temporal nonuniform L1 type difference scheme is built ...

Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation

This paper studies the convergence of a spatial semi-discretization for ...

Please sign up or login with your details

Forgot password? Click here to reset