Finite Difference Schemes for Stochastic Partial Differential Equations in Sobolev Spaces

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• 作者：Máté Gerencsér ; István Gy?ngy
• 关键词：Cauchy problem ; Stochastic PDEs ; Finite differences ; Extrapolation to the limit ; Richardson’s method ; 65M06 ; 60H15 ; 65B05
• 刊名：Applied Mathematics and Optimization
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：72
• 期：1
• 页码：77-100
• 全文大小：574 KB
• 参考文献：1.Ciaret, P.G., Lions, J.J. (eds.): Handbook of Numerical Analysis. Elsevier, Amsterdam (2013)
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• 作者单位：Máté Gerencsér (1)
  István Gy?ngy (1)
  
  1. Department of Mathematics and Statistics, University of Edinburgh, King’s Buildings, Edinburgh, EH9 3JZ, UK
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Systems Theory and Control
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  Numerical and Computational Methods
  
• 出版者：Springer New York
• ISSN：1432-0606

文摘

We discuss \(L_p\)-estimates for finite difference schemes approximating parabolic, possibly degenerate, SPDEs, with initial conditions from \(W^m_p\) and free terms taking values in \(W^m_p.\) Consequences of these estimates include an asymptotic expansion of the error, allowing the acceleration of the approximation by Richardson’s method.