William F. Mitchell Applied and Computational Mathematics Division National Institute of Standards and Technology Gaithersburg, MD, USA 20899-8910 Abstract: One aspect of adaptive mesh refinement in the finite element method for solving partial differential equations is the method by which elements are refined. In the early 1980’s the dominant method for refining triangles was the […]

Date of Online Publication: 31/03/2008 Keywords: Initial-value problem, ordinary differential equation, event location, root-finding, generalized eigenvalues, companion matrix pencil, Hermite interpolation problem,B�zout matrix Authors: Robert M. Corless, Azar Shakoori, D.A. Aruliah, Laureano Gonzalez-Vega Pages: 1-16 Continuous extensions are now routinely provided by many IVP solvers, for graphical output, error control, or event location. Recent developments

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

Keywords: predator-prey model, equilibria, stochastic diferential equation, stochastic stability. Abstract: We develop a mathematical model for understanding the e ect of wanderer spiders as biological controllers of the insects infesting vineyards, thus accounting also for the role played by residual wood and green patches as spiders habitat in the otherwise homogeneuous landscape of the Langhe

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

K. Kotrasova and E. Kormanikova Department of Structural Mechanics, Institute of Structural Engineering, Civil Engineering Faculty, Technical University of Ko?ice, 04200 Kosice, Slovakia Received 31 January, 2019; accepted in revised form 18 March, 2019 Abstract: When a rectangular tank contained liquid vibrates, the liquid exerts hydrodynamic pressure acting onto tank walls and tank bottom. This

J. Kralik and J. Kralik, jr. Department of Structural Mechanics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, 810 05 Bratislava, Slovakia Received 28/02/2020, Revised 21/07/2020, Accepted 28/10/2020 Abstract: Engineering structures are designed to resist all expected loadings without failure. However, structural failures do happen occasionally, mainly due to inadequate design and construction,

Keywords: fundamental solution method, periodic plane elasticity Abstract: We present a fundamental solution method for elasticity problems of planes with one-dimensional periodic structure, to which it is difficult to apply the conventional fundamental solution method. We propose an approximate solution of the fundamental solution method which is modi ed so that it is suitable to

J. C. Butcher2 Department of Mathematics, University of Auckland, Auckland, New Zealand Received February 8, 2010; accepted in revised form February 22, 2010. Abstract: B-series, together with the algebraic system which underpins them, are essential tools in the study of properties of numerical methods for evolutionary problems. This paper surveys the properties of these constructs