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Numerical Mathematics and Applications - 1st Edition - ISBN: 9780444700674, 9781483295671

Numerical Mathematics and Applications, Volume 1

1st Edition

Editors: J. Vignes R. Vichnevetsky
eBook ISBN: 9781483295671
Imprint: North Holland
Published Date: 1st November 1986
Page Count: 433
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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


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.


No. of pages:
© North Holland 1986
1st November 1986
North Holland
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Ratings and Reviews

About the Editors

J. Vignes

R. Vichnevetsky

Affiliations and Expertise

Rutgers University, New Brunswick, NJ, USA