Numerical Mathematics and Applications

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 ArithmeticSection 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 AlgorithmSection 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 MethodsSection 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 TheorySection 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 b