Numerical integration of ordinary differential equations with some invariants is considered. For such a purpose, certain projection methods have proved its high accuracy and efficiency, but sometimes they can exhibit instability. In this paper, a new, highly efficient projection method is proposed based on explicit Runge–Kutta methods. The key there is to employ the idea of the perturbed colloc...

An embedded diagonally implicit Range-Kutta Nystrom (RKN) method is constructed for the integration of initial value problems for second order ordinary differential equations possessing oscillatory solutions. This embedded method is derived using a three stage diagonally implicit Runge-Kutta Nystrom method of order four within which a third order three stage diagonally implicit Runge-Kutta Nyst...

This paper presents the work carried out by CALPE team on the development of a mathematical model used in the study and simulation of the pantograph-catenarydynamic interaction in high speed railways considering two independent spans ofcatenary where the transition spans are overlapped. According to the developedmathematical model, a non lineal system of differential equations with variablecons...

Abstract. In this paper we derive a class of numerical integration formulas of a parallel type for ordinary differential equations. These formulas may be used simultaneously on a set of arithmetic processors to increase the integration speed. Conditions for the convergence of such formulas are formulated. Explicit examples for two and four processor cases are derived. Results of numerical exper...

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is...

A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrr odinger equation. The formula considered contains certain free parameters which allow it to be tted automatically to exponential functions. The new methods are very simple and integrate more exponential functions than both the well known fourth order Numerov t...

A set of validated numerical integration methods based on explicit and implicit Runge-Kutta schemes is presented to solve, in a guaranteed way, initial value problems of ordinary differential equations. Runge-Kutta methods are well-known to have strong stability properties, which make them appealing to be the basis of validated numerical integration methods. A new approach to bound the local tr...

Realistic animation of soft objects such as cloth is essential for plausible character animation. Many techniques have been proposed for the simulation of soft objects, and most of them are based on numerical integration. Among the techniques, the implicit integration method is the most likely technique for realtime environments, since it allows large time steps for cloth simulation by ensuring...

This paper describes a new method of numerical integration and compares its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. By using generalized Gaussian quadratures for bandlimited functions, the implicit Runge-Kutta scheme (a collocation method) allows us to use significantly fewer force function evaluations than other integrators. The new method comput...