scholarly journals Two stage waveform relaxation method for the initial value problems of differential-algebraic equations

2011 ◽  
Vol 236 (6) ◽  
pp. 1123-1136 ◽  
Author(s):  
Wendi Bao ◽  
Yongzhong Song
Keyword(s):  
Initial Value Problems ◽  
Relaxation Method ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Initial Value ◽  
Two Stage ◽  
Waveform Relaxation Method

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 method for fractional differential-algebraic equations

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Xiao-Li Ding ◽  
Yao-Lin Jiang
Keyword(s):  
Integrated Circuits ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Relaxation Method ◽  
Differential Algebraic Equations ◽  
Iteration Scheme ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Waveform Relaxation Method ◽  
Fractional Differential

AbstractThe waveform relaxation method has been successfully applied into solving fractional ordinary differential equations and fractional functional differential equations [11, 5]. In this paper, the waveform relaxation method is further used to solve fractional differential-algebraic equations, which often arise in integrated circuits with new memory materials. We give the iteration scheme of the waveform relaxation method and analyze the convergence of the method under linear and nonlinear conditions for the right-hand of the equations. Numerical examples illustrate the feasibility and efficiency of the method.

MULTISPLITTING WAVEFORM RELAXATION FOR SYSTEMS OF LINEAR INTEGRAL-DIFFERENTIAL-ALGEBRAIC EQUATIONS IN CIRCUIT SIMULATION

2000 ◽  
Vol 10 (03n04) ◽  
pp. 205-218 ◽  
Author(s):  
YAO-LIN JIANG ◽  
RICHARD M. M. CHEN
Keyword(s):  
Convergence Rates ◽  
Circuit Simulation ◽  
Relaxation Method ◽  
Convergence Condition ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Waveform Relaxation Method ◽  
Linear Integral ◽  
Theoretical Results

The multisplitting technique introduced by D. P. O'Leary and R. E. White is applied to treat the waveform relaxation solutions for systems of linear integral-differential-algebraic equations in circuit simulation. The convergence condition of the multisplitting waveform relaxation method which can contain overlapping is established for the continuous-time case. The convergence rates of the relaxation-based method for different multisplittings are compared from the view-point of spectral radii of splitting matrices in systems. Numerical experiments are provided to confirm the new theoretical results.

scholarly journals Discrete Waveform Relaxation Method for Linear Fractional Delay Differential-Algebraic Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Hongliang Liu ◽  
Yayun Fu ◽  
Bailing Li
Keyword(s):  
Time Lag ◽  
Relaxation Method ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Convergence Results ◽  
Waveform Relaxation Method ◽  
Fractional Delay ◽  
Delay Differential

Fractional order delay differential-algebraic equations have the characteristics of time lag and memory and constraint limit. These yield some difficulties in the theoretical analysis and numerical computation. In this paper, we are devoted to solving them by the waveform relaxation method. The corresponding convergence results are obtained, and some numerical examples show the efficiency of the method.

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