2013/08/31 by Xiaojie Wang, Siqing Gan, Jingtian Tang · 1 citation
Earth and Planetary Sciences · Economics, Econometrics and Finance · #Financial Risk and Volatility Modeling #Meteorological Phenomena and Simulations #Stochastic processes and financial applications
paper · doi:10.1137/130937524
openalex publication_date 2014/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Novel fully discrete schemes are developed to numerically approximate a semilinear stochastic wave equation driven by additive space-time white noise. A spectral Galerkin method is proposed for the spatial discretization, and exponential time integrators involving linear functionals of the noise are introduced for the temporal approximation. The resulting fully discrete schemes are very easy to implement and allow for a higher strong convergence rate in time than existing time-stepping schemes such as the Crank--Nicolson--Maruyama scheme and the stochastic trigonometric method. Particularly, it is shown that the new schemes achieve in time an order of 1- ε for arbitrarily small ε >0, which exceeds the barrier order (1)/(2) established by Walsh [Illinois J. Math., 50 (2006), pp. 991--1018]. Numerical results confirm higher convergence rates and computational efficiency of the new schemes.