Stiff oscillatory systems, delta jumps and white noise
UNSPECIFIED. (2001) Stiff oscillatory systems, delta jumps and white noise. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 1 (1). pp. 69-99. ISSN 1615-3375Full text not available from this repository.
Two model problems for stiff oscillatory systems are introduced. Both comprise a linear superposition of N much greater than 1 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 N --> infinity and in the second case so that it approximates white noise. In both cases the fastest natural frequency of the oscillators is O(N). The model problems are integrated numerically in the stiff regime where the time-step Deltat satisfies NDeltat = O(1). The convergence of the algorithms is studied in this case in the limit N --> infinity and Deltat --> 0. For the white noise problem both strong and weak convergence are considered. Order reduction phenomena are observed numerically and proved theoretically.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Q Science > QA Mathematics
|Journal or Publication Title:||FOUNDATIONS OF COMPUTATIONAL MATHEMATICS|
|Official Date:||February 2001|
|Number of Pages:||31|
|Page Range:||pp. 69-99|
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