Numerical Solution of Partial Differential Equations—II, Synspade 1970

Proceedings of the Second Symposium on the Numerical Solution of Partial Differential Equations, SYNSPADE 1970, Held at the University of Maryland, College Park, Maryland, May 11-15, 1970

Bert Hubbard

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780123585028
• eBook ISBN:
  9781483262482
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

Numerical Solution of Partial Differential Equations—II: Synspade 1970 provides information pertinent to the fundamental aspects of partial differential equations. This book covers a variety of topics that range from mathematical numerical analysis to numerical methods applied to problems in mechanics, meteorology, and fluid dynamics. Organized into 18 chapters, this book begins with an overview of the methods of the Rayleigh–Ritz–Galerkin type for the approximation of boundary value problems using spline basis functions and Sobolev spaces. This text then analyzes a special approach aimed at solving elliptical equations. Other chapters consider the approximation theoretic study of special sets of approximating functions. This book discusses as well combining the alternating-direction methods with Galerkin methods to obtain highly efficient procedures for the numerical solution of second order parabolic and hyperbolic problems. The final chapter deals with the results concerning Chebyshev rational approximations of reciprocals of certain entire functions. This book is a valuable resource for mathematicians.

Table of contents

• Front Cover
• Numerical Solution of Partial Differential Equations-II: Synspade 1970
• Copyright Page
• Table of Contents
• CONTRIBUTORS
• PREFACE
• CHAPTER 1. SOME ASPECTS OF THE METHOD OF THE HYPERCIRCLE APPLIED TO ELLIPTIC VARIATIONAL PROBLEMS
• CHAPTER 2. THE FINITE ELEMENT METHOD FOR ELLIPTIC DIFFERENTIAL EQUATIONS
• CHAPTER 3. ON THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUE PROBLEMS BY LEAST SQUARES APPROXIMATION OF THE DATA
• CHAPTER 4. ALTERNATING-DIRECTION GALERKIN METHODS ON RECTANGLES
• CHAPTER 5. ON THE DIFFERENCE EQUATIONS FOR METEOROLOGICAL PREDICTION
• CHAPTER 6. FURTHER DEVELOPMENTS IN THE APPROXIMATION THEORY OF EIGENVALUES
• CHAPTER 7. NUMERICAL DESIGN OF TRANSONIC AIRFOILS
• CHAPTER 8. ON THE NUMERICAL TREATMENT OF PARTIAL DIFFERENTIAL EQUATIONS BY FUNCTION THEORETIC METHODS
• CHAPTER 9. A NEW DIFFERENCE SCHEME FOR PARABOLIC PROBLEMS
• CHAPTER 10. SINGULARITIES IN INTERFACE PROBLEMS
• CHAPTER 11. INITIAL BOUNDARY VALUE PROBLEMS FOR PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS IN ONE SPACE DIMENSION
• CHAPTER 12. NUMERICAL SOLUTION OF CONDITIONALLY PROPERLY POSED PROBLEMS
• CHAPTER 13. ON GENERAL PURPOSE PROGRAMS FOR FINITE ELEMENT ANALYSIS, WITH SPECIAL REFERENCE TO GEOMETRIC AND MATERIAL NONLINEARITIES
• CHAPTER 14. ON THE THEORY OF THE SPLITTING-UP METHOD
• CHAPTER 15. ON CLASSES OF n-DIMENSIONAL NONLINEAR MAPPINGS GENERALIZING SEVERAL TYPES OF MATRICES
• CHAPTER 16. THE FINITE ELEMENT METHOD AND APPROXIMATION THEORY
• CHAPTER 17. ON THE RATE OF CONVERGENCE OF DIFFERENCE SCHEMES FOR HYPERBOLIC EQUATIONS
• CHAPTER 18. SOME RESULTS IN APPROXIMATION THEORY WITH APPLICATIONS TO NUMERICAL ANALYSIS