An Error Embedded Runge-Kutta Method for Initial Value Problems

Runge-Kutta Pairs for Scalar Autonomous Initial Value Problems

We present the equations of condition up to sixth order for Runge-Kutta (RK) methods, when integrating scalar autonomous problems. Two RK pairs of orders 5(4) are derived. The first at a cost of only five stages per step, while the other having an extremely small principal truncation error. Numerical tests show the superiority of the new pairs over traditional ones.

An Embedded 4(3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Method for Solving Periodic Initial Value Problems

Order and Stiffness of the Gauss Runge-kutta Method for Initial-boundary Value Problems

Abstract. Existing analysis shows that when the Gauss Runge-Kutta (GRK) (also called Legendre-Gauss collocation) formulation with s Gaussian nodes is applied to ordinary differential equation initial value problems, the discretization has order 2s (super-convergent) [8]. However, for time-dependent partial differential equations (PDEs) with boundary conditions, super-convergence is only observe...

Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Abstract—In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing ...

Runge-Kutta(5,5) Methods for Robot Arm & Initial Value Problem

An ultimate aim of this present paper is to solve application problem such as robot arm and initial value problems by applying Runge-Kutta fifth order five stage numerical techniques. The calculated output for robot arm coincides with exact solution which is found to be better, suitable and feasible for solving real time problems.