Numerical renormalization-group calculations for similarity solutions and traveling waves

Lin Yuan Chen, Nigel Goldenfeld

Research output: Contribution to journalArticlepeer-review

Abstract

We present a numerical implementation of the renormalization group (RG) for partial differential equations, constructing similarity solutions and traveling waves. We show that for a large class of well-localized initial conditions, successive iterations of an approximately defined discrete RG transformation in space and time will drive the system towards a fixed point. This corresponds to a scale-invariant solution, such as a similarity or traveling-wave solution, which governs the long-time asymptotic behavior. We demonstrate that the numerical RG method is computationally very efficient.

Original languageEnglish (US)
Pages (from-to)5577-5581
Number of pages5
JournalPhysical Review E
Volume51
Issue number6
DOIs
StatePublished - Jan 1 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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