TY - GEN A1 - Lopez-Fernandez, Maria A1 - Lubich, Christian A1 - Schädle, Achim T1 - Adaptive, Fast and Oblivious Convolution in Evolution Equations with Memory N2 - To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing $N$ steps requires only $O(N\log N)$ operations and $O(\log N)$ active memory, in place of $O(N^2)$ operations and $O(N)$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schrödinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law. KW - convolution quadrature KW - adaptivity KW - Volterra integral equations KW - numerical inverse Laplace transform KW - anomalous diffusion KW - fractional order viscoelasticity Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/435 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4358 ER -