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.

Waveform relaxation methods for fractional functional differential equations

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Xiao-Li Ding ◽  
Yao-Lin Jiang
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Relaxation Method ◽  
Waveform Relaxation ◽  
Relaxation Methods ◽  
Special Cases ◽  
Waveform Relaxation Method ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

AbstractIn this paper, we use waveform relaxation method to solve fractional functional differential equations. Under suitable conditions imposed on the so-called splitting functions the convergence results of the waveform relaxation method are given. Delay dependent error estimates for the method are derived. Error bounds for some special cases are considered. Numerical examples illustrate the feasibility and efficiency of the method. It is the first time for applying the method in the fractional functional differential equations.

A multigrid waveform relaxation method for solving the poroelasticity equations

2018 ◽  
Vol 37 (4) ◽  
pp. 4805-4820 ◽  
Author(s):  
S. R. Franco ◽  
C. Rodrigo ◽  
F. J. Gaspar ◽  
M. A. V. Pinto
Keyword(s):  
Relaxation Method ◽  
Waveform Relaxation ◽  
Waveform Relaxation Method
Sign in / Sign up

Export Citation Format

Share Document