Numerical Methods for Ordinary Differential Equations

In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation....

Numerical solution of dynamical systems with equality state-space constraints

Numerical simulation of constrained dynamical systems is known to exhibit stability problems even when the unconstrained system can be simulated in a stable manner. We show that not the constraints themselves, but the transformation of a continuous set of equations to a discrete set of equations is the true source of the stability problem....

Study on efficient numerical time-integration methods for simulation of multi-body systems

This report describes the results of an evaluation of numerical integration schemes to be used for the digital simulation of second order ordinary differential equations (ODE's) which are characteristic for multibody systems such as space manipulators. The study focuses on dedicated schemes for this type of systems. Main attention is paid to the...

Viscous-inviscid interaction, partitioned dynamical systems and i(n)te(g)ration

Time-integration methods for partitioned dynamical systems and iterative methods for viscous-inviscid interaction are unified using the language of linear algebra. In this way all expertise built up in viscous-inviscid interaction methods becomes available for the integration of partitioned dynamical systems. This report applies some well...

A statistical method for error reduction in an integration process involving experimental data

The numerical integration of a non-linear function f(a (t), ap(t),.. a (t)) vith mutually independent variaties a, is considered for the case that the initial conditions for the integration process and time series of a, are determined by experiment. In order to minimize the error in the result of the integration process a technique is developed...