Summary
In a previous paper [1] a procedure for obtaining an approximate solution of the Fokker-Planck-Kolmogokov (FPK) equation, as applied to a single degree of freedom (sdof) oscillator with an unilateral barrier was proposed. Some results were obtained, showing an encouraging agreement with the results obtained via Monte Carlo simulation. In the conclusion of the same paper some ideas for further research and for improving the approximation were outlined.
In particular, the procedure requires a bivariate integration in the probability phase-space. Apart from the fact that numerical integration, as executed in that version, is very time-consuming, it was also identified as a possible source of errors, due to the difficulty in locating the significant domain of the probability functions that are to be integrated, while evolving in time. Therefore the possibility of an analytical closed-form integration is explored here, in order to evaluate also its influence on the accuracy of the results, as a first step towards the validation of the procedure.
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References
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© 1992 Springer-Verlag Berlin Heidelberg
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Baratta, A., Zuccaro, G. (1992). An Application to the Solution of the Fokker-Planck-Kolmogorov Equation for Non Linear Oscillators under Stochastic Loading. In: Bellomo, N., Casciati, F. (eds) Nonlinear Stochastic Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84789-9_4
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DOI: https://doi.org/10.1007/978-3-642-84789-9_4
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