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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
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 1985
- 1st November 1986
- North Holland
- eBook ISBN:
Rutgers University, New Brunswick, NJ, USA
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