Superlinear convergence of asynchronous multi-splitting waveform relaxation methods applied to a system of nonlinear ordinary differential equations (Q2479454)

The initial value problem defined by a system of nonlinear ordinary differential equations is reformulated as a fixed point problem of a certain operator \(T\) on a Banach space which is subsequently solved by applying an asynchronous iteration associated with \(T\) (the so-called asynchronous multi-splitting waveform relaxation). This technique generalizes the treatment introduced by \textit{A. Frommer} and \textit{B. Pohl} [Numer. Linear Algebra Appl. 2, No.~4, 335--346 (1995; Zbl 0831.65031)] for linear ordinary differential equations. The paper under review, based largely on previous results obtained by the first author, establishes the superlinear convergence of the algorithm.