20.500.12556/RUL-160915 A novel class of collocation methods based on the weighted integral form of ODEs In this work, a novel class of collocation methods for numerical integration of ODEs is presented. Methods are derived from the weighted integral form of ODEs by assuming that a polynomial function at individual time increment approximates the solution of the ODE. A distinct feature of the approach, which we demonstrated in this work, is that it allows the increase of accuracy of a method while retaining the number of method coefficients. This is achieved by applying different quadrature rule to the approximation function and the ODE, resulting in different behaviour of a method. Quadrature rules that we examined in this work are the Gauss–Legendre and Lobatto quadrature where several other quadrature rules could further be explored. The approach has also the potential for enhancing the accuracy of the established Runge–Kutta-type methods. We formulated the methods in the form of Butcher tables for convenient implementation. The performance of the new methods is investigated on some well-known stiff, oscillatory and non-linear ODEs from the literature. collocation methods numerical integration ordinary differential equations stiff systems kolokacijske metode numerična integracija navadne diferencialne enačbe trdi sistemi true false true Angleški jezik Slovenski jezik Članek v reviji 2024-09-05 12:43:14 2024-09-05 12:43:19 2025-08-08 13:33:32 0000-00-00 00:00:00 2021 0 0 28 str. iss. 4, art. 135 Vol. 40 Jun. 2021 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 2022-06-01 517.91(045) 1807-0302 10.1007/s40314-021-01506-6 62500867 Urevc,_Starman,_Macek,_Halilovic_-_A_novel_class_of_collocation_methods_based_on_the_weighted_integral_form_of_ODEs.pdf Urevc,_Starman,_Macek,_Halilovic_-_A_novel_class_of_collocation_methods_based_on_the_weighted_integral_form_of_ODEs.pdf 1 8E2A82D2C5E206ADEDF28AFB21478DF3 f4f77ac1f404c0ee9e45091f185263344e5418bf9c712fc9adf87652e18865f6 5db457a8-6c47-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=189937 https://link.springer.com/article/10.1007/s40314-021-01506-6 1 a98cac93-6b73-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=189738 Fakulteta za strojništvo 0 0 0