Difference methods for time discretization of stochastic wave equation

2021/06/07 by Xing Liu, Liu, Xing
Economics, Econometrics and Finance · Engineering · Mathematics · #26A33 #65C30 #65L20 #65M60 #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2106.03387

openalex publication_date 2021/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 L²-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 L²-norm. Several numerical experiments are provided to confirm the theoretical error estimates.

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