Janez Urevc (Author), Miroslav Halilovič (Author)

Abstract

In this paper, a new class of Runge-Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge-Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss-Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

Keywords

kolokacijske metode;Runge-Kutta metoda;numerična integracija;sistemi diferencialnih enačb;collocation methods;Runge-Kutta 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: 517.9(045)
COBISS: 47315203 Link will open in a new window
ISSN: 2227-7390
Views: 168
Downloads: 45
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: Slovenian
Secondary keywords: kolokacijske metode;Runge-Kutta metoda;numerična integracija;sistemi diferencialnih enačb;
Type (COBISS): Article
Pages: f. 1-25
Volume: ǂVol. ǂ9
Issue: ǂiss. ǂ2
Chronology: Jan. 2021
DOI: 10.3390/math9020174
ID: 14570388