Parallel implementation issues of the explicit Verlet{type (VT) and the implicit Runge{Kutta (RK) methods for molecular dynamics integration (MD) on parallel distributed memory processors with the ring topology are described and compared. Both methods are applied to a system of N particles interacting through the Lennard{Jones potential. The RK method is carried out for the two{stage fourth{ord...

‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed meth...

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 ...

An optimized explicit modified Runge-Kutta RK method for the numerical integration of the radial Schrödinger equation is presented in this paper. This method has frequency-depending coefficients with vanishing dispersion, dissipation, and the first derivative of dispersion. Stability and phase analysis of the new method are examined. The numerical results in the integration of the radial Schröd...

The conventional method of imposing time dependent boundary con itioras for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficien...

We consider the construction of a special family of Runge–Kutta (RK) collocation methods based on intra-step nodal points of Chebyshev–Gauss–Lobatto type, with A-stability and stiffly accurate characteristics. This feature with its inherent implicitness makes them suitable for solving stiff initial-value problems. In fact, the two simplest cases consist in the well-known trapezoidal rule and th...

purpose: to report the results of different methods for true corneal power and intraocular lens (iol) power calculation in 10 eyes with previous radial keratotomy (rk) with or without astigmatic keratotomy. methods: in this case series including 10 eyes of 7 patients who had undergone rk with or without astigmatic keratotomy, we firstly determined corneal power using two methods: contact lens m...

Portable RK is a portable implementation of a resource kernel, a resource-centric approach to build a real-time kernel that provides explicit timely, guaranteed and enforced access by applications to system resources [13]. Portable RK is designed to work with widely available operating systems with minimal changes. This facilitates experimentation in a familiar software environment and helps th...