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

Abstract

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.

Keywords

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

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FS - Faculty of Mechanical Engineering
UDC: 517.91(045)
COBISS: 62500867 Link will open in a new window
ISSN: 1807-0302
Views: 75
Downloads: 24
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Other data

Secondary language: Slovenian
Secondary keywords: kolokacijske metode;numerična integracija;navadne diferencialne enačbe;trdi sistemi;
Type (COBISS): Article
Embargo end date (OpenAIRE): 2022-06-01
Pages: str. 1-28
Volume: ǂVol. ǂ40
Issue: ǂiss. ǂ4
Chronology: Jun. 2021
DOI: 10.1007/s40314-021-01506-6
ID: 24920762