Issues 1-2

Blended General Linear Methods based on Boundary Value Methods in the Generalized BDF family

Issues 1-2 Volume 04

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, […]

Forty-Five Years of A-stability

Issues 1-2 Volume 04

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

Spectral Approximation of Time Windows in the Solution of Dissipative Linear Differential Equations

Issues 1-2 Volume 04

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

Simulation and Inversion of Seismic Wave Propagation on Continental Scales Based on a Spectral-Element Method

Issues 1-2 Volume 04

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

Variable Step/Order Generalized Upwind Methods for the Numerical Solution of Second Order Singular Perturbation Problems

Issues 1-2 Volume 04

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

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