Structure preserving schemes for the continuum Kuramoto model: Phase transitions

José A. Carrillo, Young Pil Choi, Lorenzo Pareschi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The construction of numerical schemes for the Kuramoto model is challenging due to the structural properties of the system which are essential in order to capture the correct physical behavior, like the description of stationary states and phase transitions. Additional difficulties are represented by the high dimensionality of the problem in presence of multiple frequencies. In this paper, we develop numerical methods which are capable to preserve these structural properties of the Kuramoto equation in the presence of diffusion and to solve efficiently the multiple frequencies case. The novel schemes are then used to numerically investigate the phase transitions in the case of identical and nonidentical oscillators.

Original languageEnglish
Pages (from-to)365-389
Number of pages25
JournalJournal of Computational Physics
Volume376
DOIs
Publication statusPublished - 2019 Jan 1

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All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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