An Accurate Polynomial Approximation of Exponential Integrators

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• 作者：A. Y. Suhov (1)
  
• 关键词：Exponential integrators ; Exponential time differencing ; Polynomial approximation ; NLS ; Nonlinear wave equation ; Reaction–diffusion equation ; 65M22 ; 65L04 ; 41A10
• 刊名：Journal of Scientific Computing
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：60
• 期：3
• 页码：684-698
• 全文大小：530 KB
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• 作者单位：A. Y. Suhov (1)
  
  1. Department of Applied Mathematics, Tel Aviv University, 69978?, Tel Aviv, Israel
  
• ISSN：1573-7691

文摘

Numerical time propagation of semi-linear equations such as reaction–diffusion, non-linear Schr?dinger or semi-linear wave equations can be performed by the use of exponential time differencing. However, the evaluation of exponential integrators poses a serious technical complexity, particularly in multiple dimensions. In this paper we approach this difficulty by deriving simple polynomial series approximations of exponential integrators. Several numerical examples are presented.