Stability of a multi-rate method for numerical integration of ODE's
type: Item
instance of: scholarly article
title: Stability of a multi-rate method for numerical integration of ODE's
zbMATH Open document ID: 0771.65037
DOI: 10.1016/0898-1221(93)90218-K
publication date: 1993-02-22T00:00:00Z
review text: The author assumes that a nonlinear initial value problem can be partitioned into two subsystems according to whether the equations characterize slow or fast responses. Two different explicit Runge-Kutta methods with different stepsizes are combined with an extrapolation of the slow-response approximation to approximate the solution of the two subsystems in tandem. The paper derives sufficient conditions for the scheme to be absolutely stable. If is found that the matrix of the test equation needs to be diagonal dominance determines the size of the stability regions. To establish the result, the author gives a detailed argument which traces the two types of components through the application of the method. After realizing for the stability analysis that the derivative evaluations are representing using a linear homogeneous system, the interested reader will be able to follow the arguments through with a little tenacity and willingness to accomodate the few typographical errors that occur.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 120315
zbMATH Keywords: multirate
zbMATH Keywords: stability regions
zbMATH Keywords: nonlinear initial value problem
zbMATH Keywords: explicit Runge-Kutta methods
zbMATH Keywords: extrapolation
author: Jan Frederick Andrus
MaRDI profile type: Publication
cites work: Numerical Solution of Systems of Ordinary Differential Equations Separated into Subsystems
cites work: Formulas for modular integration of systems of ODE's
full work available at URL: 0898-1221(93)90218-k
OpenAlex ID: W2020502171
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 120315