Issues 1-2

J. Cash Department of Mathematics, Imperial College of Science, Technology and Medicine, London, SW7 2AZ, United Kingdom   Download PDF

Date of Online Publication: 26/08/2006 Keywords: Boundary Value Problems, Ordinary Differential Equations, B-Splines, Spline Collocation, Boundary Value Methods Authors: Francesca Mazzia, Alessandra Sestini and Donato Trigiante Pages: 131-144 BS methods are a special class of Linear Multistep Methods defined using B-spline functions. These methods are always convergent and have good stability properties when used as

Date of Online Publication: 26/08/2006 Authors: J. R. Cash and S. Girdlestone Pages: 59-80 Fixed step, symmetric Runge-Kutta-Nystr�m formulae have proved to be very efficient for the numerical integration of a large class of reversible second order systems of ordinary differential equations of the special form . However for some important classes of problems it

Date of Online Publication: 26/08/2006 Authors: P. Amodio, I. Gladwell and G. Romanazzi Pages: 5-12 We generalize the cyclic reduction algorithm to the solution of Bordered ABD linear systems with blocks of different sizes and with different sizes and with different overlaps. This kind of system often arises form the numerical approximation of BVPs with

Date of Online Publication: 26/08/2006 Keywords: Boundary Value Problems, Mesh Selection, Conditioning Authors: Jeff R. Cash and Francesca Mazzia Pages: 81-90 In this paper we demonstrate how hybrid mesh selection strategies based on conditioning can be used in codes designed for the numerical solution of singularly perturbed boundary value problems. The new mesh selection strategies

Date of Online Publication: 26/08/2006 Keywords: Conditioning, stability, stiffness, dynamical systems, boundary value problems, ordinary differential equations, numerical linear algebra Authors: Felice Iavernaro, Francesca Mazzia and Donato Trigiante Pages: 91-112 The terms stability and conditioning are used with a variety of meanings in Numerical Analysis. All of them have in common the general concept of

Date of Online Publication: 26/08/2006 Authors: J. R. Cash, N. Sumarti, T. J. Abdulla and I. Vieira Pages: 49-58 There now exist several powerful codes for the numerical integration of first order systems of nonlinear two-point boundary value problems. All of these codes aim to provide a continuous solution to the problem being solved but

Date of Online Publication: 26/08/2006 Keywords: MIRK, Runge Kutta, ODE, Boundary Value Problem, Lobatto Formulae, Obrechkoff Formulae Authors: S. D. Capper, J. R. Cash and D. R. Moore Pages: 13-25 A substantial increase in efficiency may be obtained by numerical integration methods which take advantage of the special second order forms or in systems of

Date of Online Publication: 26/08/2006 Keywords: Conservative vector elds, Hamiltonian systems, symplecticity, symmetric methods Authors: Felice Iavernaro and Donato Trigiante Pages: 113-130 The use of symmetric schemes has revealed interesting stability properties for the long time simulation of conservative, and in particular Hamiltonian systems. By using one of the simplest symmetric formulae, namely the trapezoidal

Date of Online Publication: 26/08/2006 Authors: S. D. Capper and D. R. Moore Pages: 27-47 Mono-Implicit Runge-Kutta (MIRK) formulae present an effective means for solving general non-linear two-point boundary value problems. High order finite difference schemes provide significant savings in both computational time and memory when the problem exhibits the required smoothness. In this paper