Updated semi‐discretization method for periodic delay‐differential equations with discrete delay

By Tamás Insperger, Gábor Stépán. 2004

753 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7cfdb723e9ff13cf2f7653b6c262e18091be9f1a

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In Computational Theory and Mathematics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels (2009, result): “The same results were later shown for finite cutting times by Insperger and Stépán [12,13] using the semi-discretization method [14] and by Mann et al.”
Bifurcations and multiple traffic jams in a car-following model with reaction-time delay (2005, methodology): “Note that functions with similar shapes and properties to (4) were used in [2,3].”
Multiple regenerative effects in cutting process and nonlinear oscillations (2014, methodology): “2.2 From PDE–ODE system to nonlinear map based on semi-discretization method In order to solve this ordinary-partial differential system numerically, the partial differential equation is discretized into a series of ordinary differential equations based on the semi-discretization method proposed by ”
2:1 Resonance in the delayed nonlinear Mathieu equation (2007, methodology): “the DDE slow flow with an ODE slow flow, an approximation that is valid for small eT . Stability charts for the linear delayed equation with general time delay were numerically generated by Breda et al. [8] and Insperger and St´ ep´ an [ 9 ].”
A spectral element approach for the stability of delay systems (2011, methodology): “Examples of other methods that can be used for autonomous as well as non-autonomous DDEs include the semi-discretization method [32, 33], collocation-based methods [34–38], and temporal finite element analysis (TFEA) [39].”
State-dependent delay in regenerative turning processes (2006, neutral): “An efficient technique is the semi-discretization method (see [20, 21]), as it was shown in [19] for turning with varying spindle speed.”
Analysis of directional factors in milling: importance of multi-frequency calculation and of the inclusion of the effect of the helix angle (2010, methodology): “[8], Insperger and Stépán [9, 10] and Bayly et al.”