Equation-free, effective computation for discrete systems: a time stepper based approach
2005 (English)In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 15, no 3, 975-996 p.Article in journal (Refereed) Published
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be explicitly constructed. The method only uses a time-integration code for the discrete problem and judicious choices of initial data and integration times; our bifurcation computations are based on the so-called Recursive Projection Method (RPM) with arc-length continuation [Shroff & Keller, 1993]. The technique is used to monitor features of the genuinely discrete problem such as the pinning of coherent structures and its results are compared to quasi-continuum approaches such as the ones based on Pade approximations.
Place, publisher, year, edition, pages
2005. Vol. 15, no 3, 975-996 p.
equation-free methods, homogenization, discrete problems, bifurcation, pinning condition
IdentifiersURN: urn:nbn:se:kth:diva-4905DOI: 10.1142/S0218127405012399ISI: 000229230400016ScopusID: 2-s2.0-21144445075OAI: oai:DiVA.org:kth-4905DiVA: diva2:6777
Workshop on Modeling and Computations in Dynamical Systems
Budapest, HUNGARY, OCT, 2003
QC 201010152005-02-022005-02-022011-10-12Bibliographically approved