Volume 06

A Uniformly Convergent Sequence of Spline Quadratures for Cauchy Principal Value Integrals

Issues 3-4 Volume 06

C. Dagnino , V. Demichelis Department of Mathematics, Faculty of Scienze Matematiche Fisiche e Naturali, University of Torino, 10100 Torino, Italy Received 30 January, 2009; accepted in revised form 13 October, 2011 Abstract: We propose a new quadrature rule for Cauchy principal value integrals based on quadratic spline quasi-interpolants which have an optimal approximation order […]

A Complete Orthogonal System of Spheroidal Monogenics

Issues 3-4 Volume 06

J. Morais2 Freiberg University of Mining and Technology, Institute of Applied Analysis, Prueferstr. 9, 09596 Freiberg, Germany Received 26 November, 2010; accepted in revised form 28 July, 2011 Abstract: During the past few years considerable attention has been given to the role played by monogenic functions in approximation theory. The main goal of the present

Solving ODEs, DA O AEs, DDE and PD in R

Issues 1-2 Volume 06

Karline Soetaert Centre for Estuarine and Marine Ecology, Netherlands Institute of Ecology, 4401 NT Yerseke, The Netherlands Thomas Petzoldt Institut fur Hydrobiologie Technische Universitat Dresden 01062 Dresden, Germany Received 21 February, 2011; accepted in revised form 11 March, 2011 Abstract: The open-source problem solving software R [1] has become one of the most widely used

Optimal Stability of Bivariate Tensor Product B-bases

Issues 3-4 Volume 06

E. Mainar and Juan Manuel Pena Departamento de Matematica Aplicada, Universidad de Zaragoza, Zaragoza, Spain Received 15 December, 2009; accepted in revised form 18 October, 2011 Abstract: We analyze some properties of bivariate tensor product bases. In particular, we obtain conditions so that a general bivariate tensor product basis is optimally stable for evaluation. Finally,

Iterative Solution of Piecewise Linear Systems for the Numerical Solution of Obstacle Problems

Issues 3-4 Volume 06

Luigi Brugnano and Alessandra Sestini Dipartimento di Matematica “U. Dini” Viale Morgagni 67/A, 50134 Firenze, Italy Dedicated to Prof. D. Trigiante on the occasion of his 65th birthday. Received 16 December, 2009; accepted in revised form 24 September, 2011 Abstract: We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant

A Matrix Method for the Solution of Sturm-Liouville Problems

Issues 1-2 Volume 06

Pierluigi Amodio , Giuseppina Settanni Dipartimento di Matematica, Universita di Bari, I-70125 Bari, Italy Received 22 February, 2011; accepted in revised form 13 March, 2011 Abstract: We investigate the numerical solution of regular and singular Sturm-Liouville problems by means of finite difference schemes of high order. In particular, a set of differ- ence schemes is

Error Estimation via Defect Computation and Reconstruction: Some Particular Techniques

Issues 1-2 Volume 06

W. Auzinger Institute for Analysis and Scientific Computing, Vienna University of Technology, 1040 Vienna, Austria Received 20 February, 2011; accepted in revised form 10 March, 2011 Abstract: The well-known technique of defect correction can be used in various ways for estimating local or global errors of numerical approximations to differential or integral equations. In this

Random Walks on Complex Modular Networks

Issues 1-2 Volume 06

Natasa Djurdjevac , Sharon Bruckner, Tim OF Conrad, Christof Schuette Fachbereich Mathematik und Informatik Institut fuer Mathematik Freie Universitaet Berlin {djurdjev,sharonb,conrad,schuette}@math.fu-berlin.de Received 20 February, 2011; accepted in revised form 10 March, 2011 Abstract: Complex modular networks appear frequently, notably in the biological or social sciences. We focus on two current challenges regarding network modularity: the

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