An equivalent polynomial approximation technique in nonlinear structural dynamics (Q1904922)

A method is presented for approximating the joint density function \(p(x, x')\) of the solution of a nonlinear stochastic differential equation (NSDE) of the form \(x'' + g(x,x') = F(t)\), where \(F(t)\) is Gaussian white noise. The original NSDE is approximated by another more tractable NSDE whose solution's joint density function can be found and used as a very accurate approximation of \(p(x,x')\). Several examples are given in which the approximate solutions agree with approximations in the literature found by other methods.