×

On the generalization of probabilistic transformation method. (English) Zbl 1122.65304

Summary: The probabilistic transformation method with the finite element analysis is a new technique to solve random differential equation. The advantage of this technique is finding the “exact” expression of the probability density function of the solution when the probability density function of the input is known. However the disadvantage is due to the characteristics (geometrics and materials) of the analyzed structure included in the random differential equation.In this paper, a developed formula is used to generalize this technique by obtaining the “exact” joint probability density function of the solution in any situations, as well as the proposed technique for the non-linear case.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] El-Tawil, M.; El-Tahhan, W.; Hussein, A., A proposed technique of SFEM on solving ordinary random differential equation, J. Appl. Math. Comput., 35-47 (2005) · Zbl 1060.65006
[2] S. Kadry, R. Younes. Etude probabiliste d’un système mécanique à paramètres incertains par une technique basée sur la méthode de transformation, in: Proceeding of CANCAM 2004.; S. Kadry, R. Younes. Etude probabiliste d’un système mécanique à paramètres incertains par une technique basée sur la méthode de transformation, in: Proceeding of CANCAM 2004.
[3] Kadry, S.; Chateauneuf, A.; El-Tawil, K., Random eigenvalue problem of Stochastic Systems, (Proceedings of the 8th International Conference on Computational Structure Technology (2006), Civil-Comp Press: Civil-Comp Press Spain)
[4] Kadry, S.; Chateauneuf, A.; El-Tawil, K., One-dimensional transformation method in reliability analysis, (Proceedings of the 8th International Conference on Computational Structure Technology (2006), Civil-Comp Press: Civil-Comp Press Spain)
[5] Papoulis, A., Probability, Random Variables and Stochastic Processes (2002), McGraw-Hill: McGraw-Hill Boston, USA · Zbl 0191.46704
[6] Gupta, A.; Nagar, D., Matrix Variate Distributions, Monographs & Surveys in Pure & Applied Mathematics (2000), Chapman & Hall/CRC: Chapman & Hall/CRC London
[7] Soize, C., Random matrix theory and non-parametric model of random uncertainties in vibration analysis, J. Sound Vib., 263, 4, 893-916 (2003) · Zbl 1237.74097
[8] Soize, C., Non-gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators, Comput. Methods Appl. Mech. Eng., 195, 1-3, 26-64 (2006) · Zbl 1093.74065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.