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

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

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.

• Language: Slovenian
• Keywords: numerična integracija, metode Runge-Kutta, kolokacijske metode, navadne diferencialne enačbe
• Typology: 1.08 - Published Scientific Conference Contribution
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: Str. 219-224
• PID: 20.500.12556/RUL-131474
• UDC: 519.62(045)
• COBISS.SI-ID: 78095107
• Publication date in RUL: 28.09.2021

Record is a part of a monograph

• Title: Kuhljevi dnevi 2021 : zbornik del
• Editors: Janko Slavič, Martin Česnik
• Place of publishing: Ljubljana
• Publisher: Slovensko društvo za mehaniko
• Year: 2021
• ISBN: 978-961-93859-6-8
• COBISS.SI-ID: 74786051

Secondary language

• Language: English
• Title: The usage of weighted integral form for the improvement of accuracy of Runge-Kutta-type collocation methods

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.

• Keywords: numerical integration, collocation methods, Runge-Kutta methods, ordinary differential equations