Enhancing accuracy of Runge–Kutta-type collocation methods for solving ODEs

Urevc, Janez (author), Halilovič, Miroslav (author)

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.

• Language: English
• Keywords: collocation methods, Runge–Kutta methods, numerical integration, ordinary differential equations, stiff systems
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 21 str.
• Numbering: Vol. 9, iss. 2, art. 174
• PID: 20.500.12556/RUL-135061
• UDC: 517.9(045)
• ISSN on article: 2227-7390
• DOI: 10.3390/math9020174
• COBISS.SI-ID: 47315203
• Publication date in RUL: 18.02.2022

Record is a part of a journal

• Title: Mathematics
• Shortened title: Mathematics
• Publisher: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
• Licensing start date: 16.01.2021

Secondary language

• Language: Slovenian
• Keywords: kolokacijske metode, Runge-Kutta metoda, numerična integracija, sistemi diferencialnih enačb

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0263
• Name: Mehanika v tehniki