A widely used prototype phase model to describe the synchronous behavior of weakly coupled limit-cycle oscillators is the Kuramoto model whose dynamics for sufficiently large ensemble of oscillators can be effectively approximated by the corresponding mean-field equation ’the Kuramoto Sakaguchi Equation’. In the recent past, it has been extensively studied to analyze the phase transition of between different kind of ordered states.In the talk, we are going to derive and analyze a numerical method for a general class of mean-field equations, including the Kuramoto Sakaguchi equation. Along the way, we will prove the strong convergence of the scheme to the unique weak solution whenever the initial datum has bounded variation. We also show convergence in the sense of measures, thereby relaxing the assumption of bounded variation. The theoretical results will be verified with several numerical experiments.
This is a joint work with U. S. Fjordholm.