In this paper, we construct canonical explicit 5-stage and 7-stage Runge-KuttaNyström methods of orders 5 and 6, respectively, for Hamiltonian dynamical systems.

The Multistage Differential Transform Method (MDTM) is employed to solve the model for HIV infection of CD4T cells. Comparing the numerical results to those obtained by the classical fourth order Runge-Kutta method showed the preciseness and efficacy of the multistep differential transform method. The study shows that the method is a powerful and promising tool for solving coupled systems of di...

We study numerical integrators that contract phase space volume even when the ODE does so at an arbitrarily small rate. This is done by a splitting into two-dimensional contractive systems. We prove a sufficient condition for Runge–Kutta methods to have the appropriate contraction property for these two-dimensional systems; the midpoint rule is an example.  2000 IMACS. Published by Elsevier Sc...

The gravitational anomalies are investigated for generalized Euclidean Taub-NUT metrics which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. In order to evaluate the axial anomalies, the index of the Dirac operator for these metrics with the APS boundary condition is computed. The role of the Killing-Yano tensors is discussed for these two types of quantu...

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...

New Runge–Kutta–Nyström methods especially designed for the numerical integration of perturbed oscillators are presented in this paper. They are capable of exactly integrating the harmonic or unperturbed oscillator. We construct an embedded 4(3) RKN pair that is based on the FSAL property. The new method is much more efficient than previously derived RKN methods for some subclasses of problems....

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.

Explicit Runge–Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge–Kutta schemes available in literature. Furthermore, they have a small principal error n...

A new Runge-Kutta-Nyström method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this paper. The new method is based on the Dormand and Prince RungeKutta-Nyström method of algebraic order four[1]. Numerical illustrations indicate that the new method is much more efficient than the classical one.