Numerical path integration of a non-homogeneous Markov process

The numerical path integration method, based on Gauss–Legendre integration scheme, is applied to a Duffing oscillator subject to both sinusoidal and white noise excitations. The response of the system is a Markov process with one of the drift coefficients being periodic. It is a non-homogeneous Mark...

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Bibliographic Details
Published inInternational journal of non-linear mechanics Vol. 39; no. 9; pp. 1493 - 1500
Main Authors Yu, J.S., Lin, Y.K.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2004
Subjects
Markov process
Numerical method
Random vibration
Markov process
Numerical method
Random vibration
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ISSN0020-7462
1878-5638
DOI10.1016/j.ijnonlinmec.2004.02.011

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Summary:The numerical path integration method, based on Gauss–Legendre integration scheme, is applied to a Duffing oscillator subject to both sinusoidal and white noise excitations. The response of the system is a Markov process with one of the drift coefficients being periodic. It is a non-homogeneous Markov process that does not have a stationary probability distribution. When applying the numerical procedure, the values of transition probability density at the Gaussian–Legendre quadrature points need only be calculated for time steps of the first period of the sinusoidal excitation, and they can be saved for use in all subsequent periods. The numerical procedure is capable of capturing the evolution of the probability density from an initial distribution to one that is changing and rotating periodically in the phase space.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2004.02.011