Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise

2017/04/10 by Max Gunzburger, Buyang Li, Gunzburger, Max +3
Economics, Econometrics and Finance · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1704.02912

openalex publication_date 2017/04/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01

Abstract

The stochastic time-fractional equation ∂_t ψ-Δ∂_t^1-α ψ= f + W with space-time white noise W is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error estimate \mathbb E‖ψ(⋅,t_n)-ψ_n‖_L²(O)²=O(τ^1-αd/2) is established for α∈(0,2/d), where d denotes the spatial dimension, ψ_n the approximate solution at the n^{\rm th} time step, and 𝔼 the expectation operator. In particular, the result indicates optimal convergence rates of numerical solutions for both stochastic subdiffusion and diffusion-wave problems in one spatial dimension. Numerical examples are presented to illustrate the theoretical analysis.

Citations

• Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise

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