Stiff Oscillatory Systems, Delta Jumps and White Noise |
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Authors: | B Cano A M Stuart E Süli J O Warren |
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Institution: | (1) Departamento de Matemática Applicada y Computación Facultad de Ciencias Universidad de Valladolid Valladolid, Spain , ES;(2) Mathematics Institute University of Warwick Coventry CV4 7AL, UK , GB;(3) Oxford University Computing Laboratory Wolfson Building, Parks Road Oxford OX1 3QD, UK , GB;(4) Scientific Computing and Computational Mathematics Program Gates 288 Stanford University Stanford, CA 94305-9025, USA, US |
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Abstract: | Two model problems for stiff oscillatory systems are introduced. Both comprise a linear superposition of harmonic oscillators used as a forcing term for a scalar ODE. In the first case the initial conditions are chosen so that
the forcing term approximates a delta function as and in the second case so that it approximates white noise. In both cases the fastest natural frequency of the oscillators
is <e6>OM</e6>(N). The model problems are integrated numerically in the stiff regime where the time-step satisfies The convergence of the algorithms is studied in this case in the limit and For the white noise problem both strong and weak convergence are considered. Order reduction phenomena are observed numerically
and proved theoretically.
August 25, 1999. Final version received: May 3, 2000. |
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Keywords: | AMS Classification 34A65 60H10 65L70 82C80 |
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