A General Approach to Waveform Relaxation Solutions of Nonlinear Differential-Algebraic Equations: The Continuous-Time and Discrete-Time Cases

2004 ◽  
Vol 51 (9) ◽  
pp. 1770-1780 ◽  
Author(s):  
Y.-L. Jiang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations

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.

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.

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.

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