20.500.12556/RUL-129790 Numerične metode za integracijo hitro oscilirajočih funkcij delo diplomskega seminarja Numerical methods for highly oscillatory integrals V delu diplomskega seminarja si pogledamo numerične metode za integracijo hitro oscilirajočih funkcij specifičnega tipa. Podrobneje obravnavamo dva razreda metod, asimptotske metode in Filonove metode. V obeh primerih integrand ločimo na del, ki povzroča hitro oscilacijo, in del, ki ne oscilira oziroma oscilira počasi. Asimptotske metode so primerne predvsem pri zelo hitrih oscilacijah in se ločijo glede na lastnosti hitro oscilirajočega dela. Ideja Filonovih metod je, da pohleven del integranda aproksimiramo s polinomi, iz preostanka pa izpeljemo tako imenovane momente, ki se jih pod določenimi pogoji da eksaktno izračunati. Vse obravnavane metode implementiramo in preizkusimo na več numeričnih primerih, pri čemer primerjamo absolutno napako glede na različne hitrosti oscilacije. In this thesis, we look at numerical methods for the integration of highly oscillatory functions of a specific type. We discuss two classes of methods in detail, asymptotic methods and Filon Methods. In both cases, we divide the integrand into a part, which causes high oscillation, and a part that does not oscillate or oscillates slowly. Asymptotic methods are particularly suitable for very high oscillations and differ according to properties of the part, which causes high oscillation. The idea of Filon methods is that we approximate the part that does not contribute to high oscillation with polynomials, and from the rest of the integrand we derive the so-called moments, which can be calculated analitically under certain conditions. We implement all the discussed methods and test them on several numerical cases, comparing the absolute error with respect to different oscillation speeds. hitro oscilirajoče funkcije asimptotska metoda Filonove metode highly oscillatory functions asymptotic method Filon methods true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2021-09-08 08:15:06 2021-09-08 08:15:07 2024-05-29 13:55:14 0000-00-00 00:00:00 2021 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 119497 75600899 3039.pdf 3039.pdf 1 B44D23ABA3DFE98CBC484D8A49344B2D b0c929bd36a8a4064b2b3c0f798f6a76ea4306ed8fd823c22db20810a4ff427b de457118-106b-11ec-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=146819 Fakulteta za matematiko in fiziko 0 0 0