Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)

Adaptive, Fast and Oblivious Convolution in Evolution Equations with Memory

Please always quote using this URN: urn:nbn:de:0297-zib-9399
  • 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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics - number of accesses to the document
Metadaten
Author:Maria Lopez-Fernandez, Christian Lubich, Achim Schädle
Document Type:ZIB-Report
Tag:Volterra integral equations; adaptivity; anomalous diffusion; convolution quadrature; fractional order visco; numerical inverse Laplace transform
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M99 None of the above, but in this section
65-XX NUMERICAL ANALYSIS / 65Rxx Integral equations, integral transforms / 65R20 Integral equations
Date of first Publication:2006/11/02
Series (Serial Number):ZIB-Report (06-45)
ZIB-Reportnumber:06-45
Published in:Appeared in: SIAM Journal on Scientific Computing Vol.30, No.2 (2008)
DOI:https://doi.org/10.1137/060674168
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.