Analysis of the heterogeneous multiscale method for ordinary differential equations

By W. E. 2003

115 citations recorded by the source corpus.

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Heterogeneous Multiscale Methods: A Review (2007, methodology): “10), it is a simple matter to prove [53]:”
NUMERICAL TECHNIQUES FOR MULTI-SCALE DYNAMICAL SYSTEMS WITH STOCHASTIC EFFECTS ⁄ (2003, unknown): “Finally, evaluating the expectation in (2.5) via time-averaging amounts to using as estimator B̂(X̂εn, ε) = 1 M M−1∑ m=0 f(X̂εn, Ẑ ε n,m, ε).”
Modulated Fourier expansions and heterogeneous multiscale methods (2009, methodology): “a(t) = vmax ω cosωt; (2) vmax > 0 measures the maximum value of the velocity v(t) = vmax sinωt of the pivot and ω 1 is the ‘large’ parameter in the perturbation analysis that follows.”
Analysis of multiscale methods for stochastic differential equations (2005, methodology): “Deterministic analogs of the algorithm were analyzed in [4, 8].”
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, unknown): “22 3.5 FLAVORS for generic stiff SDEs . . . . . . . . . . . . . . . . . . . . . . . 23”
A mathematical framework of the bridging scale method (2006, background): “On the other hand, clear mathematical formulations and careful analysis are desired for applications and further improvements [23, 24].”