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.

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 Semigroups and evolutionary equations

2021 ◽  
Author(s):  
Sascha Trostorff
Keyword(s):  
Initial Value Problem ◽  
Differential Algebraic Equations ◽  
Delay Equation ◽  
Algebraic Equations ◽  
Infinite Dimensions ◽  
Initial Value ◽  
Evolutionary Equations ◽  
Strongly Continuous Semigroups ◽  
Initial States

AbstractWe show how strongly continuous semigroups can be associated with evolutionary equations. For doing so, we need to define the space of admissible history functions and initial states. Moreover, the initial value problem has to be formulated within the framework of evolutionary equations, which is done by using the theory of extrapolation spaces. The results are applied to two examples. First, differential-algebraic equations in infinite dimensions are treated and it is shown, how a $$C_{0}$$ C 0 -semigroup can be associated with such problems. In the second example we treat a concrete hyperbolic delay equation.

Discrete-Time Inverse Dynamics Control of Flexible Joint Robots

1992 ◽  
Vol 114 (2) ◽  
pp. 229-233 ◽  
Author(s):  
K. P. Jankowski ◽  
H. Van Brussel
Keyword(s):  
Discrete Time ◽  
Control Algorithm ◽  
Inverse Dynamics ◽  
Differential Algebraic Equations ◽  
Control Methods ◽  
Algebraic Equations ◽  
Computationally Efficient ◽  
Electromechanical Actuators ◽  
Flexible Joint Robots ◽  
Inverse Dynamics Control

This paper focuses on the problem of the application of inverse dynamics control methods to robots with flexible joints and electromechanical actuators. Due to drawbacks of the continuous-time inverse dynamics, discussed in the paper, a new control strategy in discrete-time is presented. The proposed control algorithm is based on numerical methods conceived for the solution of index-three systems of differential-algebraic equations. The method is computationally efficient and admits low sampling frequencies. The results of numerical experiments confirm the advantages of the designed control algorithm.

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.

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