甘四清

教授 博士生导师 硕士生导师

所在单位:数学与统计学院

学历:博士研究生毕业

办公地点:中南大学数学与统计学院446办公室

性别:男

联系方式:邮箱:sqgan@csu.edu.cn。

学位:博士学位

在职信息:在职

毕业院校:中国科学院 数学与系统科学研究院 数学研究所

学科:数学

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A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations

发布时间:2020-06-28

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发表刊物:Applied Numerical Mathematics

关键字:Stochastic partial differential equations; Invariant measure; Ergodicity; Weak approximation; Exponential Euler scheme

摘要:We discrete the ergodic semilinear stochastic partial differential equations in space dimension d ≤3with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the spatial semi-discretization and the spatio-temporal full discretization are ergodic. Further, convergence orders of the numerical invariant measures, depending on the regularity of noise, are recovered based on an easy time-independent weak error analysis without relying on Malliavin calculus. To be precise, the convergence order is 1-epsilon in space and 1/2-epsilon in time for the space-time white noise case and 2 -epsilon in space and 1-epsilon in time for the trace class noise case in space dimension d =1, with arbitrarily small epsilon>0. Numerical results are finally reported to confirm these theoretical findings.

合写作者:Chen Ziheng, Gan Siqing, Wang Xiaojie

论文类型:期刊论文

文献类型:J

卷号:157

页面范围:135–158

是否译文:

发表时间:2020-06-15

收录刊物:SCI

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