20.500.12556/RUL-135061 Enhancing accuracy of Runge–Kutta-type collocation methods for solving ODEs 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. collocation methods Runge–Kutta methods numerical integration ordinary differential equations stiff systems kolokacijske metode Runge-Kutta metoda numerična integracija sistemi diferencialnih enačb true false true Angleški jezik Slovenski jezik Članek v reviji 2022-02-18 16:17:34 2022-02-18 16:17:36 2022-09-14 04:11:28 0000-00-00 00:00:00 2021 0 0 21 str. iss. 2, art. 174 Vol. 9 Jan. 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.9(045) 2227-7390 10.3390/math9020174 47315203 RAZ_Urevc_Janez_2021.pdf RAZ_Urevc_Janez_2021.pdf 1 E633106A0090EBA9D5667A49FBCDA2E3 ed37642a1922e7daddb1d041a318e1227038197db5e19eccc0951d1d682596c3 e5e9aa92-90cd-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153912 https://www.mdpi.com/2227-7390/9/2/174 1 a840d58d-90cd-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153911 Fakulteta za strojništvo 0 0 0