1. Enhancing accuracy of Runge–Kutta-type collocation methods for solving ODEs
- Author
-
Janez Urevc and Miroslav Halilovič
- Subjects
Differential equation ,General Mathematics ,stiff systems ,Runge-Kutta metoda ,010103 numerical & computational mathematics ,Type (model theory) ,01 natural sciences ,Mathematics::Numerical Analysis ,Computer Science (miscellaneous) ,Applied mathematics ,0101 mathematics ,Engineering (miscellaneous) ,Runge–Kutta methods ,Mathematics ,Nonlinear ode ,Physics::Computational Physics ,sistemi diferencialnih enačb ,Collocation ,lcsh:Mathematics ,Ode ,lcsh:QA1-939 ,Computer Science::Numerical Analysis ,Numerical integration ,010101 applied mathematics ,kolokacijske metode ,Ordinary differential equation ,udc:517.9(045) ,collocation methods ,ordinary differential equations ,numerical integration ,numerična integracija - Abstract
In this paper, a new class of Runge&ndash, 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&ndash, Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss&ndash, 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.
- Published
- 2022