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Fast and oblivious convolution quadrature

Please always quote using this URN: urn:nbn:de:0297-zib-8437
  • We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N\, \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the convolution kernel, but instead $O(\log N)$ evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation with transparent boundary conditions.

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Metadaten
Author:Achim Schädle, Maria Lopez-Fernandez, Christian Lubich
Document Type:ZIB-Report
Tag:Runge-Kutta methods; Volterra integral equation; anomalous diffusion; convolution; numerical integration
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Rxx Integral equations, integral transforms / 65R20 Integral equations
Date of first Publication:2005/01/24
Series (Serial Number):ZIB-Report (05-09)
ZIB-Reportnumber:05-09
Published in:Appeared in:SIAM J. Sci. Comput. Vol. 28(2) (2005) 421-438
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