Cover Image
Read Now

Numerical Solution of Partial Differential Equations

This book is the result of two courses of lectures given at the University of Cologne in Germany in 1974/75. The majority of the students were not familiar with partial differential equations and functional analysis. This explains why Sections 1, 2, 4 and 12 contain some basic material and results f...

Full description

Bibliographic Details
Main Authors: Meis, T., Marcowitz, U. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1981, 1981
Edition:1st ed. 1981
Series:Applied Mathematical Sciences
Subjects:
Mathematical Analysis
Analysis
Numerical Analysis
Analysis (mathematics)
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. Initial value problems for hyperbolic and parabolic differential equations
  • 1. Properly posed initial value problems
  • 2. Types and characteristics
  • 3. Characteristic methods for first order hyperbolic systems
  • 4. Banach spaces
  • 5. Stability of difference methods
  • 6. Examples of stable difference methods
  • 7. Inhomogeneous initial value problems
  • 8. Difference methods with positivity properties
  • 9. Fourier transforms of difference methods
  • 10. Initial value problems in several space variables
  • 11. Extrapolation methods
  • II. Boundary value problems for elliptic differential equations
  • 12. Properly posed boundary value problems
  • 13. Difference methods
  • 14. Variational methods
  • 15. Hermite interpolation and its application to the Ritz method
  • 16. Collocation methods and boundary integral methods
  • III. Solving systems of equations
  • 17. Iterative methods for solving systems of linear and nonlinear equations
  • 18. Overrelaxation methods for systems of linear equations
  • 19. Overrelaxation methods for systems of nonlinear equations
  • 20. Band width reduction for sparse matrices
  • 21. Buneman Algorithm
  • 22. The Schröder-Trottenberg reduction method
  • Appendices: Fortran programs
  • Appendix 0: Introduction
  • Appendix 1: Method of Massau
  • Appendix 2: Total implicit difference method for solving a nonlinear parabolic differential equation
  • Appendix 3: Lax-Wendroff-Richtmyer method for the case of two space variables
  • Appendix 4: Difference methods with SOR for solving the Poisson equation on nonrectangular regions
  • Appendix 5: Programs for band matrices
  • Appendix 6: The Buneman algorithm for solving the Poisson equation

Similar Items