A NEW IMPROVED RUNGE-KUTTA FORMULA FOR DIRECTLY SOLVING $z''(t)=g(t,z,z')$

Improved Runge-Kutta Methods for Solving Ordinary Differential Equations (Penambahbaikan Kaedah Runge-Kutta untuk Menyelesaikan Persamaan Pembezaan Biasa)

In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical RungeKutta method. Therefore the new scheme is computationally more efficient at achieving the same order of local accuracy. The order conditions of the new methods...

Embedded explicit Runge – Kutta type methods for directly solving special third order differential equations

Fifth 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...

Runge-Kutta Method for Solving Uncertain Differential Equations

*Correspondence: [email protected] Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China Abstract Uncertain differential equations have been widely applied to many fields especially to uncertain finance. Unfortunately, we cannot always get the analytic solution of uncertain differential equations. Early researchers have put up a numerical method based on t...

Runge - Kutta Methods page RK 1 Runge - Kutta Methods

Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...