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 […]
A. Duangpan1 and R. Boonklurb2 1,2Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand Received 27 March, 2019; accepted in revised form 28 April, 2020 Abstract: Several boundary value problems are de ned on complex shaped domains, such as pentagonal, circular, L-shaped, butter y, peanut-shaped and elliptic domains. These irregular
Keywords: Helly’s theorem; set of width; set of constant width Mathematics Subject Classifcation: 52A01 Abstract: In this paper, we prove that, for a given positive number d, if every n + 1 of a collection of compact convex sets in IEn contain a set of width d (a set of constant width d, respectively) simultaneously,
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
V.V. Kozhevnikov Technological Research Institute of Ulyanovsk State University, 1/4 Universitetskaya Naberezhnaya, Ulyanovsk, 432017, Russia Received: 31 May 2019; accepted in revised form: 18 June 2019 Abstract An approach to the mathematical modeling of cognitive digital automata (CDA) is proposed. This approach represents a further development of the theory of digital automata and is based
Date of Online Publication: 31/03/2008 Keywords: Nonlinear algebraic equations, Newton’s method, problem-solving environment Authors: Raymond J. Spiteri and Thian-Peng Ter Pages: 123-137 Nonlinear algebraic equations (NAEs) occur routinely in many scientific and engineering problems. The process of solving these NAEs involves many challenges, from finding a suitable initial guess to choosing an appropriate convergence criterion.
T.V. Karpukhina1, V.N. Kovalnogov1,2, M.S. Boyarkin1 1Department of Heat-and-Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, SevernyVenets Street 32, 432027 Ulyanovsk, Russian Federation 2Scientific and Educational Center “Digital Industry”, South Ural State University, 76 Lenin Ave., 454080 Chelyabinsk, Russian Federation Received 10 March, 2020; Accepted in revised form 23 March, 2020 Abstract The
V. Ruas, A.P. Brasil, J.H. Carneiro de Araujo Received 14 December, 2010; accepted in revised form 25 April, 2012 Abstract: A three-field finite element scheme designed for solving systems of partial dif- ferential equations governing stationary viscoelastic flows is studied. It is based on the simulation of a time-dependent behavior. Once a classical time-discretization is
Date of Online Publication: 31/03/2008 Keywords: Maple, C, Code Conversion, Code Optimization Authors: Allan Wittkopf Pages: 167-180 In this article we discuss the advantages (and pitfalls) in developing code optimization and Maple to C conversion programs for Maple procedures, specifically those required for numerical differential equation solution. Special treatment related to code optimization for large
Date of Online Publication: 31/03/2008 Keywords: Differential algebraic equations (DAEs), structural analysis, Taylor series, automatic differentiation Authors: Nedialko S. Nedialkov, Nedialko S. Nedialkov Pages: 61-80 The authors have developed a Taylor series method for solving numerically an initial-value problem differential algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit,