A Chebyshev collocation based sequential matrix exponential method for the generalized density evolution equation. (January 2021)

• Record Type: Journal Article
• Authors: Zhang, Hui; Xu, Yazhou
• Is Part Of: Probabilistic engineering mechanics. Volume 63(2021)
• Publication Date: 2021-01
• Subjects: Probability density evolution method -- Spectral method -- Chebyshev polynomial -- Collocation -- Matrix exponential; Engineering -- Statistical methods -- Periodicals; Mechanics, Applied -- Statistical methods -- Periodicals; Probabilities -- Periodicals; Ingénierie -- Méthodes statistiques -- Périodiques; Mécanique appliquée -- Méthodes statistiques -- Périodiques; Probabilités -- Périodiques; 620.100727
• DOI: 10.1016/j.probengmech.2021.103118
• Languages: English
• ISSNs: 0266-8920

Abstract

Abstract: In perspective of global approximation, this study presents a numerical method for the generalized density evolution equation (GDEE) based on spectral collocation. A sequential matrix exponential solution based on the Chebyshev collocation points is derived in consideration of the coefficient or velocity term of GDEE being constant in each time step, then the numerical procedure could be successively implemented without implicit or explicit difference schemes. The results of three numerical examples indicate that the solutions in terms of the sequential matrix exponential method for GDEE have good agreement with the analytical results or Monte Carlo simulations. For sufficiently smooth cases, there need no more than one hundred representative points to achieve a satisfied solution by the proposed method, whereas for the case in presence of severe discontinuity a few more sampling points are required to keep numerical stability and accuracy.