Error analysis of exponential integrators for oscillatory second-order differential equations
نویسندگان
چکیده
منابع مشابه
Error analysis of exponential integrators for oscillatory second-order differential equations
In this paper we analyse a family of exponential integrators for secondorder differential equations in which high-frequency oscillations in the solution are generated by a linear part. Conditions are given which guarantee that the integrators allow second-order error bounds independent of the product of the step size with the frequencies. Our convergence analysis generalises known results on th...
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Article history: Received 3 March 2013 Received in revised form 6 August 2013 Accepted 12 August 2013 Available online 26 August 2013
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Numerical integrators for second-order differential equations with time-dependent high frequencies are proposed and analysed. We derive two such methods, called the adiabatic midpoint rule and the adiabatic Magnus method. The integrators are based on a transformation of the problem to adiabatic variables and an expansion technique for the oscillatory integrals. They can be used with far larger ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2006
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/39/19/s10