A fast numerical method for the cauchy problem for the smoluchowski equation

S. A. Matveev, A. P. Smirnov, E. E. Tyrtyshnikov

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

A new solution technique is proposed for one-dimensional Smoluchowski equations. It is based on the finite-difference predictor-corrector scheme and is faster than other methods using this kind of scheme. The new technique capitalizes on low-rank approximations of matrices arising after discretization of the coagulation kernel and includes a new fast convolution algorithm with the trapezoidal quadrature rule. For the grids with N nodes, the complexity of the new method is O(Nlog N) for each step with time instead of O(N2) operations required by the standard implementation of the predictor-corrector scheme.

Original languageEnglish
Pages (from-to)23-32
Number of pages10
JournalJournal of Computational Physics
Volume282
DOIs
Publication statusPublished - 1 Feb 2015
Externally publishedYes

Keywords

  • Cross matrix interpolations
  • Fast algorithms of linear algebra
  • Predictor-corrector scheme
  • Smoluchowski coagulation equation

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