A new path integration procedure based on Gauss-Legendre scheme

Jiang, Yu; Cai, Guoqiang; Ye, Lin

doi:10.1016/s0020-7462(96)00096-0

Cited by 110 publications

(37 citation statements)

References 6 publications

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“…Numerical solutions to the Fokker-Planck equations and first-passage problems (e.g. Naess and Johnson 1993;Spencer and Bergman 1993;Kloeden et al 1994;Yu et al 1997) should also be noted. These citations are, of course, far from comprehensive.…”

Section: Discussionmentioning

confidence: 99%

Some recent advances in the theory of random vibration

2002

Naturwissenschaften

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A brief introduction is first given of the history of the technical field of random vibration, tracing back to the works of physicists since the beginning of the twentieth century. This is then followed by an account of more recent developments, with emphasis on nonlinear and quasi-nonlinear systems, and on analytical solutions for the associated Fokker-Planck equation and the generalized Pontryagin equation. The governing equation of a quasi-nonlinear system is linear, but with one or more randomly varying coefficients. The techniques for finding exact probability solutions, approximate probability solutions, conditions for motion stability, and the failure probability and statistics of a system are discussed.

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Section: Discussionmentioning

confidence: 99%

Some recent advances in the theory of random vibration

2002

Naturwissenschaften

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“…for practical values of interest, that is values of probability density down to 10\. Naess and Johnsen [11] and Yu et al [13] have used the path integral method produce accurate results to probability density levels of 10\. Figure 6 shows that by increasing the number of grid points such that N "N "61, and increasing the domain limits to !8)125 )x )8)125 and !6)5 )x )6)5 , the proposed method yields accurate results down to very low probability levels.…”

Section: Duffing Oscillatormentioning

confidence: 99%

“…'s that are non-negative, enabling high-accuracy solutions to be obtained at the tails. Recently, Yu et al [13] combined the PIM with a Gauss}Legendre scheme and obtained excellent results for a Du$ng oscillator down to p.d.f. values of 10\.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Stationary FPK Equation Using Shannon Wavelets

McWilliam

Knappett

Fox

2000

Journal of Sound and Vibration

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“…Early application of the path integration to solving FPK equation was made by Wehner and Wolfer [36]. Recent improvements of the technique can be found in references [37,38].…”

Section: Solution Of Averaged Fpk Equationmentioning

confidence: 99%