Issues 1-2

Adjoint Sensitivity Analysis of Neutral Delay Differential Models

Issues 1-2 Volume 05

Fathalla A. Rihan2 Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, 17551, UAE Received 11 October, 2009; accepted in revised form 21 January, 2010 Abstract: In this short paper, we investigate sensitivity and robustness of neutral delay differential models to small perturbations in the parameters that occur in the models, […]

Hamiltonian Boundary Value Methods (Energy Preserving Discrete Line Integral Methods)

Issues 1-2 Volume 05

Luigi Brugnano3 Dipartimento di Matematica “U.Dini”, Universit`a di Firenze Viale Morgagni 67/A, I-50134 Firenze, Italy Felice Iavernaro4 Dipartimento di Matematica, Universit`a di Bari Via Orabona 4, I-70125 Bari, Italy Donato Trigiante5 Dipartimento di Energetica “S.Stecco”, Universit`a di Firenze Via Lombroso 6/17, I-50134 Firenze, Italy Received October 25, 2009; accepted in revised form April 15, 2010.

Energy-Preserving Variant of Collocation Methods

Issues 1-2 Volume 05

E. Hairer3 Universit�e de Gen`eve, Section de Math�ematiques, 2-4 rue du Li`evre, CH-1211 Gen`eve 4, Switzerland Received 15 October, 2009; accepted in revised form 21 March, 2010 Abstract: We propose a modification of collocation methods extending the ‘averaged vector field method’ to high order. These new integrators exactly preserve energy for Hamiltonian systems, are of

Explicit Implementation of Collocation Methods for Stiff Systems with Complex Spectrum

Issues 1-2 Volume 05

B. V. Faleichik2 Computational Mathematics Department, Faculty of Applied Mathematics and Computer Science, Belarusian State University, 220030 Minsk, Belarus Received October 21, 2009; accepted in revised form January 19, 2010. Abstract: Currently there are two general ways to solve stiff differential equations numerically. The first approach is based on implicit methods and the second uses

On Conjugate B-series and Their Geometric Structure

Issues 1-2 Volume 05

Abstract: The characterizations of B-series of symplectic and energy preserving integrators are well-known. The graded Lie algebra of B-series of modified vector fields include the Hamiltonian and energy preserving cases as Lie subalgebras, these spaces are relatively well understood. However, two other important classes are the integrators which are conjugate to Hamiltonian and energy preserving

High Order Finite Difference Schemes for the Solution of Second Order Initial Value Problems

Issues 1-2 Volume 05

Pierluigi Amodio2, Giuseppina Settanni3 Dipartimento di Matematica, Universit`a di Bari, I-70125 Bari, Italy Received 22 February, 2010; accepted in revised form 13 April, 2010 Abstract: The numerical solution of second order ordinary differential equations with initial conditions is here approached by approximating each derivative by means of a set of finite difference schemes of high

Towards a Definition of Equilibration for Markov Chains

Issues 1-2 Volume 05

Robert D. Skeel2 Department of Computer Science, Purdue University, West Lafayette, Indiana 47907-2107, U.S.A. Received 26 February, 2010; accepted in revised form 11 May, 2010 Abstract: Markov chain Monte Carlo methods are very popular for computing expectations. Their efficiency and reliability are subject to two significant drawbacks. The first is the correlation between successive samples.

Computing on Virtual Slow Manifolds of Fast Stochastic Systems

Issues 1-2 Volume 05

C. W. Gear,2 D. Givon and I. G. Kevrekidis Department of Chemical Engineering, Princeton University, Princeton, NJ, USA Received 10 January, 2010; accepted in revised form 20 March, 2010 Abstract: The persistently fast evolutionary behavior of certain differential systems may have intrinsically slow features. We consider systems whose solution trajectories are slowly changing distributions and

The New MATLAB Code bvpsuite for the Solution of Singular Implicit BVPs1

Issues 1-2 Volume 05

G. Kitzhofer, O. Koch, G. Pulverer, Ch. Simon, and E.B. Weinm�uller2 Institute for Analysis and Scientific Computing (E101), Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria Received 21 January, 2010; accepted in revised form 23 March, 2010 Abstract: Our aim is to provide the open domain MATLAB code bvpsuite for the efficient numerical

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