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A novel class of collocation methods based on the weighted integral form of ODEs
ID Urevc, Janez (Avtor), ID Starman, Bojan (Avtor), ID Maček, Andraž (Avtor), ID Halilovič, Miroslav (Avtor)

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Izvleček
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.

Jezik:Angleški jezik
Ključne besede:collocation methods, numerical integration, ordinary differential equations, stiff systems
Vrsta gradiva:Članek v reviji
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FS - Fakulteta za strojništvo
Status publikacije:Objavljeno
Različica publikacije:Recenzirani rokopis
Leto izida:2021
Št. strani:28 str.
Številčenje:Vol. 40, iss. 4, art. 135
PID:20.500.12556/RUL-160915-a914a38b-e543-8a0f-388a-7cbdf5a4d658 Povezava se odpre v novem oknu
UDK:517.91(045)
ISSN pri članku:1807-0302
DOI:10.1007/s40314-021-01506-6 Povezava se odpre v novem oknu
COBISS.SI-ID:62500867 Povezava se odpre v novem oknu
Datum objave v RUL:05.09.2024
Število ogledov:218
Število prenosov:79
Metapodatki:XML DC-XML DC-RDF
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Gradivo je del revije

Naslov:Computational & applied mathematics
Skrajšan naslov:Comput. appl. math.
Založnik:Springer Nature, Sociedade Brasileira de Matemática Aplicada e Computacional
ISSN:1807-0302
COBISS.SI-ID:520491801 Povezava se odpre v novem oknu

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:kolokacijske metode, numerična integracija, navadne diferencialne enačbe, trdi sistemi

Projekti

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:P2-0263
Naslov:Mehanika v tehniki

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