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Analysis of the heterogeneous multiscale method for ordinary differential equations. (English) Zbl 1088.65552

From the summary: We analyze the heterogeneous multiscale method (HMM) for ordinary differential equations with multiple time scales. The analysis is an application of the general principle discussed by W. E and B. Engquist [The heterogeneous multiscale methods. Comm. Math. Sci. 1, No. 1, 86–134 (2003)], which states that HMM is stable if the macroscale solver is stable and the total error is a sum of the standard truncation error of the macroscale solver and the error in the \(F\)-estimator. Our analysis gives a fairly detailed understanding of how the error in the \(F\)-estimator depends on various components of HMM, such as the microscale solver and the filter, as well as the nature of the microscale problem.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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