Numerical Mathematics and Applications

Numerical Mathematics and Applications

1st Edition - November 1, 1986

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  • Editors: J. Vignes, R. Vichnevetsky
  • eBook ISBN: 9781483295671

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IMACS Transactions on Scientific Computation – 85, Volume I: Numerical Mathematics and Applications contains papers on theoretical and applied aspects of numerical mathematics presented at the 11th IMACS World Congress on Scientific Computation, held in Oslo, Norway on August 5-9, 1985. The book focuses on the processes, methodologies, and approaches involved in computer arithmetic. The selection first highlights the use of CESTAC method in the parallel computation of roots of polynomials, CESTAC, and reducing abbreviation errors in iterative resolution of linear systems. Discussions focus on notations and theoretical processes, sequence of iterates in floating-point arithmetic, perturbation method, and CESTAC tested on algorithm and numerical results. The book then takes a look at optimal termination criterion and accuracy tests in mathematical programming; use of the normed residue to check the quality of the solution of a linear system; and computable bounds for solutions of integral equations. The manuscript examines arbitrarily accurate boundaries for solutions of ODEs with initial values using variable precision arithmetic and remarks on some modified Romberg algorithms for numerical integration. Topics include speed of convergence and a priori truncation error estimates, acceleration of convergence, extrapolation schemes, and the initial boundary value problem. The selection is a dependable source of data for mathematicians and researchers interested in numerical mathematics and applications.

Table of Contents

  • Section I Accuracy of Computation

    The Use of the Cestac Method in the Parallel Computation of Roots of Polynomials

    Cestac, A Tool for a Stochastic Round-Off Error Analysis in Scientific Computing

    Reducing Abbreviation Errors in Iterative Resolution of Linear Systems

    Optimal Termination Criterion and Accuracy Tests in Mathematical Programming

    On the Use of the Normed Residue to Check the Quality of the Solution of a Linear System

    Computable Bounds for Solutions of Integral Equations

    Arbitrarily Accurate Boundaries for Solutions of ODEs with Initial Values Using Variable Precision Arithmetic

    Section II Approximations and Algorithms

    Remarks on Some Modified Romberg Algorithms for Numerical Integration

    Linear and Quasilinear Extrapolation Algorithms

    Vector Padé Approximants

    Three Computational Aspects of Continued Fraction/Padé Approximants

    An Universal Conversational Program for Computing Sequences of Padé Approximants in the Non Normal Case

    Efficient Computation of a Group of Close Eigenvalues for Integral Operators

    Data Flow Analysis of Orthogonal Properties on the Conjugate Gradient and the Lanczos Algorithm

    Section III Solution of ODE's and PDE's

    Efficient Preconditionings for Matrix Problems Resulting from High Order Methods for Partial Differential Equations

    Variable Step Size / Variable Order PDE Solver with Global Optimisation

    Approximate Practical Stability for Nonlinear Evolution PDEs

    Current Methods for Large Stiff ODE Systems

    Exponential-Fitted Methods for Stiff Ordinary Differential Equations

    Linearized D-Mapping for Stiff Computations

    On the Use of Newton's Method in the Adaptive Solution of Nonlinear Two-Point Boundary Value Problems

    Spline Approximations in Numerical Method of Lines Solution of First-Order Hyperbolic Partial Differential Equations

    Some Insights into the Stability of Difference Approximations for Hyperbolic Initial-Boundary-Value Problems

    Use of a Dynamic Grid Adaption in the ASWR-Method

    The Solution of an Elliptic PDE with Periodic Boundary Conditions in a Rectangular Region

    A Modified Galerkin Scheme for Elliptic Equations with Natural Boundary Conditions

    Numerical Grid Generation through Second Order Differential-Geometric Models

    Factorization and Path Integration of the Helmholtz Equation: Numerical Algorithms

    A General Ergun Equation for a Multilayered Porous Medium

    Iterative Solutions of Problems with Shocks

    The Lumped Mass Finite Element Method for Parabolic Equations

    The Solution of Burgers' Equation by Boundary Value Methods

    Section IV Computational Acoustics

    Numerical Models for Ocean Acoustic Modes

    The Relation of the Parabolic Equation Method to the Adiabatic Mode Approximation

    A Survey of Numerical Methods for a New Class of Nonlinear Partial Differential Equations Arising in Nonspherical Geometrical Optics

    Wide Angle Parabolic Approximations in Underwater Acoustics

    The Application of the Boundary Integral Element Method to the Problem of Scattering of Sound Waves by an Elastic Wedge

    A Wave Propagation Computation Technique Using Function Theoretic Representation

    Compensating for Wavefront Turning in Wavefront Curvature Ranging

    Changes in Eigenvalues due to Bottom Interaction Using Perturbation Theory

    Section V Computational Fluid Dynamics

    Computational Fluid Dynamics, Convergent or Asymptotic

    Highly Accurate Shock Flow Calculations with Moving Grids and Mesh Refinement

    Modified Equation Methods for One-Dimensional Flame Propagation Problems

    Numerical Solution of Time-Dependent Incompressible Flows

    Pseudocharacteristic Method of Lines Simulation of Single- and Two-Phase One-Dimensional Flow Transients

    Lagrangian Modeling of Turbulent Dispersion in Shear Layers

    Studies in a Shallow Water Fluid Model Topography

    Computation of the Fine Vortex Structures of Fluids

    Inviscid Vortex Flow Simulations by Megacell Solutions to the Euler Equations

    Transonic Potential Flows: Improved Accuracy by Using Local Grids

    Numerical Analysis of Unsteady Wake Development Behind an Impulsively Started Cylinder in Slightly Viscous Fluid

    Numerical Treatment of Shocks in Unsteady Potential Flow Computation

    Generalized Vortex Methods for Stratified Layered Flows

    A Two-Fluid Model of Turbulence Applied to Simulation of Fires

    Numerical Prediction of Turbulent Flow Over a Surface-Mounted Cube

    Numerical Modelling of Air Flow in Confined Tapered Duct Inlets

    Subsurface Fluid Dynamics and Transport Phenomena Based on a Vector Representation

    Author Index

Product details

  • No. of pages: 433
  • Language: English
  • Copyright: © North Holland 1986
  • Published: November 1, 1986
  • Imprint: North Holland
  • eBook ISBN: 9781483295671

About the Editors

J. Vignes

R. Vichnevetsky

Affiliations and Expertise

Rutgers University, New Brunswick, NJ, USA

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