Numerical Approximation of Partial Differential Equations (North-holland Mathematical Library)

✍ Scribed by Eduardo L. Ortiz (editor)

• Publisher: Elsevier Science Ltd
• Year: 1987
• Tongue: English
• Leaves: 447
• Category: Library

✦ Synopsis

This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the discussion of their application to concrete problems relevant to engineering and science. Special consideration has been given to innovative numerical techniques and to the treatment of three-dimensional and singular problems. These topics are discussed in several of the invited papers. The contributed papers are divided into five parts: techniques of approximation theory which are basic to the numerical treatment of differential equations; numerical techniques based on discrete processes; innovative methods based on polynomial and rational approximation; variational inequalities, conformal transformation and asymptotic techniques; and applications of differential equations to problems in science and engineering.

✦ Table of Contents

Numerical Approximation of Partial Differential Equations
Copyright Page
Preface
Contents
INVITED PAPERS
Chapter 1. Recent Progress in the Two-Dimensional Approximation of Three Dimensional Plate Models in Nonlinear Elasticity
Chapter 2. Formulation of Alternating-Direction Iterative Methods for Mixed Methods in Three Space
Chapter 3. Iterative Methods for Singular Systems
Chapter 4. On Different Numerical Methods to Solve Singular Boundary Problems
Chapter 5. Some Numerical Techniques for the Solution of Problems Related to Semiconductor Devices
Chapter 6. Recent Progress in the Numerical Treatment of Singular Problems for Partial Differential Equations with Techniques Based on the Tau Method
Chapter 7. Present State and New Trends in Parallel Computation
Chapter 8. Finite Element Methods for Treating Problems Involving Singularities, with Applications to Linear Elastic Fracture
Chapter 9. Finite Element Solution of the Fundamental Equations of Semiconductor Devices
CONTRIBUTED PAPERS
PART I: RESULTS ON COMPUTATIONAL LINEAR ALGEBRA
Chapter 10. On Aitken-Neville Formulae for Multivariate Interpolation
Chapter 11. On Some Methods for the Construction of Smoothing Splines
Chapter 12. Generalized L-Splines as Solutions of an N-Point Boundary Value Problem
Chapter 13. Computing Errorbounds for Eigenpairs Using the Precise Scalarproduct
Chapter 14. Some Results on the AOR Iterative Method
Chapter 15. On the Speed of Convergence of the Total Step Method in Interval Computations
PART II: DISCRETE VARIABLE METHODS
Chapter 16. On the Stability of Variable Stepsize Adams Methods in Nordsieck Form
Chapter 17. The Preconditioned Conjugate Gradient Method for Solving Elliptic difference Equations
Chapter 18. Accelerated Monotone Scheme for Finite Difference Equations Concerning Steady-State Prey–Predator Interactions
Chapter 19. A Note on Three-Term Recurrences and their Numerical Treatment
Chapter 20. Mixed Finite Elements Methods for Convection-Diffusion Problems
Chapter 21. Numerical Methods of Solution of Evolution Equations of Hyperbolic Type
Chapter 22. Some Aspects of the Numerical Solution of Evolution Equations by the Method of Discretization in Time
PART III: POLYNOMIAL AND RATIONAL APPROXIMATION METHODS
Chapter 23. Some Results of the Spectrum of Chebyshev Differencing Operator
Chapter 24. On a New Boundary Element Spectral Method
Chapter 25. On Rational Approximation to Semigroups of Linear Operators
Chapter 26. A Quick Survey of Recent Developments and Applications of the T-Method
Chapter 27. Cubic and Quintic Spline Extrapolated Collocation Methods for Two-Point Boundary Value Problems
Chapter 28. Piecewise Polynomial Approximations for Cauchy Singular lntegrodifferential Equations
PART IV: VARIATIONAL METHODS AND SPECIAL TECHNIQUES
Chapter 29. Methods of Computation of Critical Points of Nonlinear Functionals
Chapter 30. Numerical Solutions of Degenerate and Pseudoparabolic Variational Inequalities
Chapter 31. Numerical Conformal Mapping Techniques for the Solution of Two-Dimensional Laplacian Boundary Value Problems
Chapter 32. Linear Approximation, Asymptotic Expansion and Mixed Problem for Some Semi-Linear Wave Equations in I Dimension
PART V: APPLICATIONS
Chapter 33. Application of the Characteristics Method with Variable Time-Step to Steady-State Convection-Diffusion Problems
Chapter 34. Homogeneization of Slightly Compressible lnviscid Flows
Chapter 35. Continuation of Periodic Solutions in Ordinary Differential Equations with Application to the Hodgkin-Huxley Model
Chapter 36. A Newton/BI-Conjugate Gradient Continuation Procedure for Buoyancy Flows
Chapter 37. IST Numerical Schemes for Nonlinear Evolution Equations of Physical Interest