A novel class of collocation methods based on the weighted integral form of ODEs

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

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
• UDK: 517.91(045)
• ISSN pri članku: 1807-0302
• DOI: 10.1007/s40314-021-01506-6
• COBISS.SI-ID: 62500867
• Datum objave v RUL: 05.09.2024

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

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