2018/05/19 by Jialin Hong, Hong, Jialin, Chuying Huang +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Biology Tumor Growth #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1805.07537
openalex publication_date 2018/05/19 · openalex created_date 2019/06/14 · openalex updated_date 2026/07/28
For semilinear stochastic evolution equations whose coefficients are more general than the classical global Lipschitz, we present results on the strong convergence rates of numerical discretizations. The proof of them provides a new approach to strong convergence analysis of numerical discretizations for a large family of second order parabolic stochastic partial differential equations driven by space-time white noises. We apply these results to the stochastic advection-diffusion-reaction equation with a gradient term and multiplicative white noise, and show that the strong convergence rate of a fully discrete scheme constructed by spectral Galerkin approximation and explicit exponential integrator is exactly \frac12 in space and \frac14 in time. Compared with the optimal regularity of the mild solution, it indicates that the spetral Galerkin approximation is superconvergent and the convergence rate of the exponential integrator is optimal. Numerical experiments support our theoretical analysis.