Higher-Order Averaging, Formal Series and Numerical Integration III: Error Bounds
نویسندگان
چکیده
منابع مشابه
Higher-Order Averaging, Formal Series and Numerical Integration III: Error Bounds
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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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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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 describe how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what we call its higher order numerical ranges. We prove some of their basic properties and describe explain how to compute them. We finally use them to obtain new spectral insights into the non-selfadjoint Anderson model in one and two space dimensions. keywords: non-self-adjoint operator, spectrum, num...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2013
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-013-9175-7