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BIT Numerical Mathematics

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11.10.2018

Stable application of Filon–Clenshaw–Curtis rules to singular oscillatory integrals by exponential transformations

verfasst von: Hassan Majidian

Erschienen in: BIT Numerical Mathematics | Ausgabe 1/2019

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Abstract

Highly oscillatory integrals, having amplitudes with algebraic (or logarithmic) endpoint singularities, are considered. An integral of this kind is first transformed into a regular oscillatory integral over an unbounded interval. After applying the method of finite sections, a composite modified Filon–Clenshaw–Curtis rule, recently developed by the author, is applied on it. By this strategy the original integral can be computed in a more stable manner, while the convergence orders of the composite Filon–Clenshaw–Curtis rule are preserved. By introducing the concept of an oscillation subinterval, we propose algorithms, which employ composite Filon–Clenshaw–Curtis rules on rather small intervals. The integral outside the oscillation subinterval is non-oscillatory, so it can be computed by traditional quadrature rules for regular integrals, e.g. the Gaussian ones. We present several numerical examples, which illustrate the accuracy of the algorithms.

Vorheriger Artikel Optimal quotients for solving large eigenvalue problems

Nächster Artikel The time-fractional diffusion inverse problem subject to an extra measurement by a local discontinuous Galerkin method

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Titel: Stable application of Filon–Clenshaw–Curtis rules to singular oscillatory integrals by exponential transformations
verfasst von: Hassan Majidian
Publikationsdatum: 11.10.2018
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 1/2019
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-018-0730-0

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