Issues 1-2

Keywords: Numerical methods for ordinary differential equations, General Linear Methods, Boundary Value Methods (BVMs), Generalized Backward Differentiation Formulae (GBDF), Blended Implicit Methods, blended iteration. Abstract: Among the methods for solving ODE-IVPs, the class of General Linear Methods (GLMs) is able to encompass most of them, ranging from Linear Multistep Formulae (LMF) to RK formulae. Moreover, […]

F. Iavernaro3 Dipartimento di Matematica, Universita di Bari, I-70125 Bari, Italy D. Trigiante Dipartimento di Energetica, Universita di Firenze, I-50134 Firenze, Italy Received 11 March, 2009; accepted in revised form 23 April, 2009 Dedicated to John Butcher on the occasion of his 75th birthday Abstract: We define a class of arbitrary high order symmetric one-step

Keywords: Stiff problems, A-stability, stability barriers, order stars, order arrows, nonlinear stability. Abstract: We discuss two events with profound implications on the way initial value problems are solved numerically. The first was the identification of stiffness as a widely spread phenomenon affecting the ability to obtain useful results. The second was the definition of A-stability

Keywords: Linear differential systems, time window, spectral approximation, waveform relaxation. Abstract: We establish a relation between the length T of the integration window of a linear differential equation x’+Ax = b and a spectral parameter s*. This parameter is determined by comparing the exact solution x(T) at the end of the integration window to the

Keywords: seismic tomography, spectral-element method, adjoint-method, Australia Abstract: We propose a novel technique for seismic waveform tomography on continental scales. This is based on the fully numerical simulation of wave propagation in complex Earth models, the inversion of complete waveforms and the quantification of the waveform discrepancies through a specially designed phase misfit. The numerical

Keywords: Two-point Boundary Value Problems, singular perturbation problems, finite difference schemes, upwind method, mesh variation. Abstract: We propose a simple and quite efficient code to solve singular perturbation problems when the perturbation parameter ? is very small. The code is based on generalized upwind methods of order ranging from 4 to 10 and uses highly