Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Symbols
- Part I Numerical Linear Algebra
- Part II Constructive Approximation Theory
- Part III Nonlinear Equations and Optimization
- Part IV Initial Value Problems for Ordinary Differential Equations
- Part V Boundary and Initial Boundary Value Problems
- 23 Boundary and Initial Boundary Value Problems for Partial Differential Equations
- 24 Finite Difference Methods for Elliptic Problems
- 25 Finite Element Methods for Elliptic Problems
- 26 Spectral and Pseudo-Spectral Methods for Periodic Elliptic Equations
- 27 Collocation Methods for Elliptic Equations
- 28 Finite Difference Methods for Parabolic Problems
- 29 Finite Difference Methods for Hyperbolic Problems
- Appendix A Linear Algebra Review
- Appendix B Basic Analysis Review
- Appendix C Banach Fixed Point Theorem
- Appendix D A (Petting) Zoo of Function Spaces
- References
- Index
23 - Boundary and Initial Boundary Value Problems for Partial Differential Equations
from Part V - Boundary and Initial Boundary Value Problems
Published online by Cambridge University Press: 29 September 2022
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Symbols
- Part I Numerical Linear Algebra
- Part II Constructive Approximation Theory
- Part III Nonlinear Equations and Optimization
- Part IV Initial Value Problems for Ordinary Differential Equations
- Part V Boundary and Initial Boundary Value Problems
- 23 Boundary and Initial Boundary Value Problems for Partial Differential Equations
- 24 Finite Difference Methods for Elliptic Problems
- 25 Finite Element Methods for Elliptic Problems
- 26 Spectral and Pseudo-Spectral Methods for Periodic Elliptic Equations
- 27 Collocation Methods for Elliptic Equations
- 28 Finite Difference Methods for Parabolic Problems
- 29 Finite Difference Methods for Hyperbolic Problems
- Appendix A Linear Algebra Review
- Appendix B Basic Analysis Review
- Appendix C Banach Fixed Point Theorem
- Appendix D A (Petting) Zoo of Function Spaces
- References
- Index
Summary
This chapter is a collection of facts, ideas, and techniques regarding the analysis of boundary value, initial and initial boundary value problems for partial differential equations. We begin by deriving some of the representative equations of mathematical physics, which then give rise to the classification of linear, second order, constant coefficient partial differential equations into: elliptic, parabolic, and hyperbolic equations. For each one of these classes we then discuss the main ideas behind problem with them and the existence of solutions: both classical and weak.
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- Classical Numerical AnalysisA Comprehensive Course, pp. 611 - 663Publisher: Cambridge University PressPrint publication year: 2022