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....

A geometrical interpretation of the addition of nodes to an interpolatory quadrature rule while preserving positive weights

A novel mathematical framework is derived for the addition of nodes to univariate and interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde matrix describing the relation between the nodes and the weights and can be used to determine all nodes that can be added to an interpolatory...

Generating nested quadrature rules with positive weights based on arbitrary sample sets

For the purpose of uncertainty propagation a new quadrature rule technique is proposed that has positive weights, has high degree, and is constructed using only samples that describe the probability distribution of the uncertain parameters. Moreover, nodes can be added to the quadrature rule, resulting in a sequence of nested rules. The rule...

A fibre flexure: Lumped shear model for masonry structures

Existing sophisticated numerical micro- and macro models have already proven to be capable of simulating typical masonry behaviour. However, assessing the global response of masonry buildings using brick-to-brick micro modelling or even simplified macro modelling, in which masonry is regarded as a continuum material, takes such an amount of time...

Computational Methods for the Long-Term Propagation of Space Debris Orbits

Space debris poses a significant problem for the space sector. This problem relates to potential collisions of debris objects with active satellites, which in many cases will lead to catastrophic damage. Due to the absence of natural decay mechanisms in the higher regions of space, debris objects in these regions have very long orbital lifetimes...

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...

Integration of plasticity equations for singular yield functions

Comparison of boundary layer calculations for the root section of a wing

At the workshop nine participants presented the results of their calculations for a practical test case. The test case deals with the 3D turbulent boundary layer development, including separation, on the root section of a swept wing. The employed calculation methods comprise 3D integral methods as well as field methods. A short description of...

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...