Journal of Computational and Nonlinear Dynamics · 2012 · 22 citations · 36 references
Natural SciencesComputational EngineeringMathematicsComputational MechanicsDifferential EquationsDynamical SystemsComputational DynamicsNumerical Methods For Differential EquationsNumerical StabilityStability TheoryTime Delay EffectsTime IntegrationChebyshev ApproximationChebyshev PolynomialsDelay Differential SystemsDelay-dependent Stability AnalysisDelay-induced Stability AnalysisMonodromy MatricesMonodromy MatrixStability Of Delay Differential Equations
Abstract In this paper, the analysis of delay differential equations with periodic coefficients and discontinuous distributed delay is carried out through discretization by the Chebyshev spectral continuous time approximation (ChSCTA). These features are introduced in the delayed Mathieu equation with discontinuous distributed delay which is used as an illustrative example. The efficiency of stability analysis is improved by using shifted Chebyshev polynomials for computing the monodromy matrix, as well as the adaptive meshing of the parameter plane. An idea for a method for numerical integration of periodic DDEs with discontinuous distributed delay based on existing MATLAB functions is proposed.
36