Janez Urevc (Avtor), Bojan Starman (Avtor), Andraž Maček (Avtor), Miroslav Halilovič (Avtor)

Povzetek

In this work, a novel class of collocation methods for numerical integration of ODEs is presented. Methods are derived from the weighted integral form of ODEs by assuming that a polynomial function at individual time increment approximates the solution of the ODE. A distinct feature of the approach, which we demonstrated in this work, is that it allows the increase of accuracy of a method while retaining the number of method coefficients. This is achieved by applying different quadrature rule to the approximation function and the ODE, resulting in different behaviour of a method. Quadrature rules that we examined in this work are the Gauss-Legendre and Lobatto quadrature where several other quadrature rules could further be explored. The approach has also the potential for enhancing the accuracy of the established Runge-Kutta-type methods. We formulated the methods in the form of Butcher tables for convenient implementation. The performance of the new methods is investigated on some well-known stiff, oscillatory and non-linear ODEs from the literature.

Ključne besede

kolokacijske metode;numerična integracija;navadne diferencialne enačbe;trdi sistemi;collocation methods;numerical integration;ordinary differential equations;stiff systems;

Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL FS - Fakulteta za strojništvo
UDK: 517.91(045)
COBISS: 62500867 Povezava se bo odprla v novem oknu
ISSN: 1807-0302
Št. ogledov: 759
Št. prenosov: 163
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Sekundarni jezik: Slovenski jezik
Sekundarne ključne besede: kolokacijske metode;numerična integracija;navadne diferencialne enačbe;trdi sistemi;
Vrsta dela (COBISS): Članek v reviji
Konec prepovedi (OpenAIRE): 2022-06-01
Strani: str. 1-28
Letnik: ǂVol. ǂ40
Zvezek: ǂiss. ǂ4
Čas izdaje: Jun. 2021
DOI: 10.1007/s40314-021-01506-6
ID: 24920762