Extension of eigenfunction-expansion solutions of a fokker-planck equation--II. Second order system

Abstract

In an earlier paper the authors presented results for eigenfunction-expansion solutions to the forward Fokker-Planck equation associated with a specific, non-linear, first-order system subject to white noise excitation. This work is concerned with eigenfunction-expansion solutions to the forward and backward Fokker-Planck equations associated with a specific, non-linear, second-order system subject to white noise excitation. Expansion terms through the fourth-order have been generated using a digital computer. Using this new information, inverted Domb-Sykes plots revealed a pattern in the coefficients for certain values of the parameters. Through this pattern, Dingle's theory of terminants was used to recast the series into a more favorable computational form.