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

Janez Urevc (Avtor), Miroslav Halilovič (Avtor)

Povzetek

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.

Ključne besede

kolokacijske metode;Runge-Kutta metoda;numerična integracija;sistemi diferencialnih enačb;collocation methods;Runge-Kutta methods;numerical integration;ordinary differential equations;stiff systems;

Podatki

Jezik:	Angleški jezik
Leto izida:	2021
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FS - Fakulteta za strojništvo
UDK:	517.9(045)
COBISS:	47315203
ISSN:	2227-7390
Št. ogledov:	168
Št. prenosov:	45
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	kolokacijske metode;Runge-Kutta metoda;numerična integracija;sistemi diferencialnih enačb;
Vrsta dela (COBISS):	Članek v reviji
Strani:	f. 1-25
Letnik:	ǂVol. ǂ9
Zvezek:	ǂiss. ǂ2
Čas izdaje:	Jan. 2021
DOI:	10.3390/math9020174
ID:	14570388