Abstract
A numerical integration scheme based on closed Newton–Cotes formulas is first proposed for calculating the response statistics of a dynamic system under Gaussian white noise excitation. Accurate system response results down to very low probability levels have been obtained by utilizing the high-degree closed Newton–Cotes formulas for the numerical integration algorithm. The computational efficiency of the numerical integration scheme is found to be very high. The proposed Newton–Cotes scheme is also compared with the Gauss–Legendre scheme in the existing literature. It is found that the Newton–Cotes algorithm is easy to develop because Newton–Cotes quadrature uses values of the integrand at equally-spaced abscissas and the values of the quadrature coefficients are easily calculated.
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