scholarly journals A Transient Stability Numerical Integration Algorithm for Variable Step Sizes Based on Virtual Input

Energies ◽  
2017 ◽  
Vol 10 (11) ◽  
pp. 1736 ◽  
Author(s):  
Yifan Gao ◽  
Jianquan Wang ◽  
Tannan Xiao ◽  
Daozhuo Jiang
Keyword(s):  
Numerical Integration ◽  
Transient Stability ◽  
Integration Algorithm ◽  
Variable Step

On Passive Non-Iterative Variable-Step Numerical Integration of Mechanical Systems for Haptic Rendering

2008 ◽  
Author(s):  
Dongjun Lee ◽  
Ke Huang
Keyword(s):  
Numerical Integration ◽  
Mechanical Systems ◽  
Haptic Rendering ◽  
Haptic Device ◽  
Integration Step ◽  
Constant Mass ◽  
Supply Rate ◽  
Integration Algorithm ◽  
Collision Handling ◽  
Variable Step

This paper consists of three parts. First, with a slightly-different, yet, more physically-plausible, discrete supply-rate (i.e. power), we propose a non-iterative (i.e. fast) and variable-step numerical integration algorithm for (scalar) discrete-passive mechanical systems, consisting of constant mass and damper, and a certain class of nonlinear spring. In the second part, we propose a fast passive collision handling algorithm with a spring-damper type virtual wall, which, to detect exact time of contacts, requires at most three intermediate non-iterative computations within each integration-step. We then propose a way of how to passively connect this discrete-passive, non-iterative, and variable-step mechanical integrators (with passive collision handling) to a continuous haptic device.

Sensitivity Analysis and Optimization of Mechanical System Design

1988 ◽  
Author(s):  
W. J. Langner
Keyword(s):  
Linear Equation ◽  
Mechanical System ◽  
Numerical Integration ◽  
Equation System ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Governing Equations ◽  
Integration Algorithm ◽  
Linear Equation System ◽  
The Matrix

Abstract The paper follows studies on simulation of three-dimensional mechanical dynamic systems with the help of sparse matrix and stiff integration numerical algorithms. For sensitivity analyses and the application of numerical optimization procedures it is substantial to calculate the effect of design parameters on the system behaviour by means of derivatives of state variables with respect to the design parameters. For static and quasi static analyses the computation of these derivatives from the governing equations leads to a linear equation system. The matrix of this set of linear equations shows to be the Jacobian matrix required in the numerical integration process solving the system of governing equations for the mechanical system. Thus the factorization of the matrix perfomed by the numerical integration algorithm can be reused solving the linear equation system for the state variable sensitivities. Some example demonstrate the simplicity of building the right hand sides of the linear equation system. Also it is demonstrated that the procedure proposed neatly fits into a modular concept for simulation model building and analysis.

A varying time-step explicit numerical integration algorithm for solving motion equation

2005 ◽  
Vol 18 (2) ◽  
pp. 239-244
Author(s):  
Zheng-hua Zhou ◽  
Yu-huan Wang ◽  
Quan Liu ◽  
Xiao-tao Yin ◽  
Cheng Yang
Keyword(s):  
Numerical Integration ◽  
Motion Equation ◽  
Time Step ◽  
Integration Algorithm

scholarly journals Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
D. Olvera ◽  
A. Elías-Zúñiga ◽  
L. N. López de Lacalle ◽  
C. A. Rodríguez
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Numerical Integration ◽  
Delay Differential Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Integration Algorithm ◽  
Homotopy Perturbation ◽  
Delay Differential

We expand the application of the enhanced multistage homotopy perturbation method (EMHPM) to solve delay differential equations (DDEs) with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.

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