A Fifth Order Runge-Kutta RK(5, 5) Method With Error Control
نویسندگان
چکیده
منابع مشابه
A Fourth Order Multirate Runge-Kutta Method with Error Control
To integrate large systems of ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on embedded, explicit Runge-Kutta (RK) formulas. The order of accuracy of such methods depends on interpolating certain solution components with a polynomial of sufficiently high degree. By analyzing the method applied to a simple test eq...
متن کاملNonstandard explicit third-order Runge-Kutta method with positivity property
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...
متن کاملA Linearly Fourth Order Multirate Runge-Kutta Method with Error Control
To integrate large systems of locally coupled ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on the Cash-Karp Runge-Kutta (RK) formula. The order of multirate methods often depends on interpolating certain solution components with a polynomial of sufficiently high degree. By using cubic interpolants and analyzing ...
متن کاملA family of fifth-order Runge-Kutta pairs
The construction of a Runge-Kutta pair of order 5(4) with the minimal number of stages requires the solution of a nonlinear system of 25 order conditions in 27 unknowns. We define a new family of pairs which includes pairs using 6 function evaluations per integration step as well as pairs which additionally use the first function evaluation from the next step. This is achieved by making use of ...
متن کاملFifth Order Improved Runge-Kutta Method for Solving Ordinary Differential Equations
Abstract: In this paper, the fifth order Improved Runge-Kutta method (IRK5) that uses just five function evaluations per step is developed. The method proposed here are derived with only five stages which results in lower number of function evaluations. Therefore, IRK5 has a lower computational cost than the classical fifth order Runge-Kutta method (RK5). Here, the order conditions of the metho...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Computer Mathematics
سال: 2002
ISSN: 0020-7160,1029-0265
DOI: 10.1080/00207160213937