Higher-Order Averaging, Formal Series and Numerical Integration II: The Quasi-Periodic Case
نویسندگان
چکیده
منابع مشابه
Erratum to: Higher-Order Averaging, Formal Series and Numerical Integration II: The Quasi-Periodic Case
The paper considers non-autonomous oscillatory systems of ordinary differential equations with d ≥ 1 nonresonant constant frequencies. Formal series like those used nowadays to analyze the properties of numerical integrators are employed to construct higher-order averaged systems and the required changes of variables. With the new approach, the averaged system and the change of variables consis...
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We show how B-series may be used to derive in a systematic way the analytical expressions of the high-order stroboscopic averaged equations that approximate the slow dynamics of highly oscillatory systems. For first-order systems we give explicitly the form of the averaged systems with O( j ) errors, j = 1,2,3 (2π denotes the period of the fast oscillations). For second-order systems with large...
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In earlier papers, it has been shown how formal series like those used nowadays to investigate the properties of numerical integrators may be used to construct highorder averaged systems or formal first integrals of Hamiltonian problems. With the new approach the averaged system (or the formal first integral) may be written down immediately in terms of (i) suitable basis functions and (ii) scal...
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The efficient construction of higher-order interlaced polynomial lattice rules introduced recently in [6] is considered and the computational performance of these higher-order QMC rules is investigated on a suite of parametric, highdimensional test integrand functions. After reviewing the principles of their construction by the “fast component-by-component” (CBC) algorithm due to Nuyens and Coo...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2012
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-012-9118-8