Uporaba utežene integralske formulacije za izboljšanje natančnosti kolokacijskih metod tipa Runge-Kutta

Janez Urevc (Author), Primož Rus (Author), Miroslav Halilovič (Author)

Abstract

V tem delu je predstavljen nov razred metod tipa Runge-Kutta (RK) za numerično reševanje navadnih diferencialnih enačb (NDE). V primerjavi s klasičnimi metodami RK izpeljava metod temelji na uteženi integralni obliki NDE. Pristop omogoča povečanje natančnosti uveljavljenih kolokacijskih metod tipa RK ob ohranjanju enakega števila stopenj metode (t.j. ob enakem številu koeficientov metode). Obnašanje metod je prikazano na analitičnem (testnem) in numeričnem primeru.

Keywords

numerična integracija;metode Runge-Kutta;kolokacijske metode;navadne diferencialne enačbe;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	UL FS - Faculty of Mechanical Engineering
UDC:	519.62(045)
COBISS:	78095107
Views:	176
Downloads:	40
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	ǂThe ǂusage of weighted integral form for the improvement of accuracy of Runge-Kutta-type collocation methods
Secondary abstract:	In this work, a new class of Runge-Kutta (RK) type colocation methods for numerical integration of ordinary differential equations (ODE) is presented. Compared to classical RK methods, the derivation of methods is based on the weighted integral form of ODE. The approach makes it possible to increase the accuracy of established RK-type collocation methods while retaining the same number of methodʼs stages (i.e., the number of methodʼs coefficients). The behaviour of methods is demonstrated on an analytical (test) and numerical example.
Secondary keywords:	numerical integration;collocation methods;Runge-Kutta methods;ordinary differential equations;
Pages:	Str. 219-224
ID:	13571118