Fast and oblivious convolution quadrature

Details Fast and oblivious convolution quadrature Fast and oblivious convolution quadrature

2005-04-22

arxiv.org/abs/math/0504461v1

SISC Vol. 28 (2), 421-438, (2006)

Mathematics

Numerical Analysis

Scientific paper

10.1137/050623139

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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