Numerical Methods for Engineers and Scientists

By W. Ames, C. Brezinski. 2008

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Cubature Kalman Filtering for Continuous-Discrete Systems: Theory and Simulations (2010, methodology): “of summary statistics in terms of conditional moments after discretizing the Itô-type process equation using the Euler or higher-order Runge-Kutta methods [23], [30].”
High-performance model reduction techniques in computational multiscale homogenization (2014, methodology): “In the spirit of classical polynomial quadrature, such as Newton–Cotes formulae [36], the modal coeﬃcients c ad 2 R n r and c in 2 R n u are determined by ﬁtting the low-dimensional approximation (54) to the weighted stresses calculated at the pre-speciﬁed sampling points.”
Wavelet Scattering Regression of Quantum Chemical Energies (2016, methodology): “3 can be improved by utilizing higher order Newton–Cotes numerical integration schemes [26], in which case one can show that for an arbitrary δ′ > 0 independent of δ, there exists O( −(1+δ )) quadratic Fourier invariants that regress U(ρ) to accuracy O( 1−δ); some additional remarks along these line”