Convergence and comparisons of waveform relaxation methods for initial value problems of linearODE systems

Computing ◽  
1993 ◽  
Vol 50 (4) ◽  
pp. 337-352 ◽  
Author(s):  
Y. Song
Keyword(s):  
Initial Value Problems ◽  
Waveform Relaxation ◽  
Initial Value ◽  
Relaxation Methods

scholarly journals On the Convergence of Continuous-Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yongxiang Zhao ◽  
Li Li
Keyword(s):  
Singular Perturbation ◽  
Continuous Time ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Relaxation Method ◽  
Waveform Relaxation ◽  
Initial Value ◽  
Relaxation Methods ◽  
Waveform Relaxation Method ◽  
Time Waveform

This paper extends the continuous-time waveform relaxation method to singular perturbation initial value problems. The sufficient conditions for convergence of continuous-time waveform relaxation methods for singular perturbation initial value problems are given.

scholarly journals General relaxation methods for initial-value problems with application to multistep schemes

2020 ◽  
Vol 146 (4) ◽  
pp. 875-906
Author(s):  
Hendrik Ranocha ◽  
Lajos Lóczi ◽  
David I. Ketcheson
Keyword(s):  
Initial Value Problems ◽  
Initial Value ◽  
Relaxation Methods

Multi-Splitting Waveform Relaxation Methods for Solving the Initial Value Problem of Linear Integral-Differential-Algebraic Equations

2011 ◽  
Vol 403-408 ◽  
pp. 1763-1766
Author(s):  
Xiao Lin Lin ◽  
Yuan Sang ◽  
Hong Wei ◽  
Li Ming Liu ◽  
Yu Mei Wang ◽  
...  
Keyword(s):  
Spectral Radius ◽  
Discrete Time ◽  
Initial Value Problem ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Initial Value ◽  
Relaxation Methods ◽  
Discrete Time Case ◽  
Linear Integral

We present the multi-splitting waveform relaxation (MSWR) methods for solving the initial value problem of linear integral-differential-algebraic equations. Based on the spectral radius of the derived operator by decoupled process, a convergent condition is proposed for the MSWR method. Finally we discussed the convergent condition of discrete-time case of MSWR.

Sign in / Sign up

Export Citation Format

Share Document