Date of Online Publication: 31/03/2008 Keywords: Ordinary differential equations; initial value problems; numerical differential, equations; numerical integration; extrapolation methods; rounding error accumulation; NDSolve Authors: Mark Sofroniou, Giulia Spaletta Pages: 105-121 This article outlines design and implementation details of the framework for one step methods for solving ordinary differential equations in Mathematica. The solver breaks up […]

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

Beny Neta * Naval Postgraduate School Department of Applied Mathematics Monterey, CA 93943 e-mail: bneta@nps.edu, Tel: 1-831-656-2235, Fax: 1-831-656-2355 Received 01/02/2020, Revised 10/12/2020, Accepted 02/03/2021 Abstract: A new trigonometrically-fitted method of order 12 is developed and compared to an existing P-stable method of the same order. Our method fit exactly the sine and cosines functions

O. Ozturk Department of Mathematics, Faculty of Arts and Sciences, Bitlis Eren University, 13000 Bitlis, Turkey Received 10 October, 2016; accepted in revised form 22 March, 2018 Abstract: Fractional calculus and its generalizations are used for the solutions of some classes of differential equations and fractional differential equations. In this paper, our aim is to

Abstract: The characterizations of B-series of symplectic and energy preserving integrators are well-known. The graded Lie algebra of B-series of modified vector fields include the Hamiltonian and energy preserving cases as Lie subalgebras, these spaces are relatively well understood. However, two other important classes are the integrators which are conjugate to Hamiltonian and energy preserving

Vasileios Chatziioannou1 1Department of Music Acoustics, University of Music and Performing Arts Vienna, Austria Received: 22 August 2017 ; Accepted in revised form: 22 January 2020 Abstract: Energy methods for constructing time-stepping algorithms are of increased in- terest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system

Keywords: Backward Difference Formula; Circuit simulation; Differential-algebraic equations; Discretization error; Multirate; Numerical time integration; Partitioning; Transient analysis Abstract: Transient analysis is an important circuit simulation technique. The circuit model, which is a system of differential-algebraic equations, is solved for a given initial condition using numerical time integration techniques. Multirate methods are efficient if the dynamical

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

Date of Online Publication: 14/04/2007 Keywords: Cell nuclei, Computational stochastic methods, Gibbs point processes, Lattice processes, Dislocations of crystals, Pseudolikelihood, Spatial arrangement, Strauss process Authors: J. Mateu Pages: 79-102 Data showing spatial structure often arise in many applied scientific fields in form of points spatially distributed within a planar region. The basic methodology for analyzing

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