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
26 - Spectral and Pseudo-Spectral Methods for Periodic Elliptic 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
Periodic differential equations and their approximation are the topic of this chapter. We discuss the application of classical finite difference schemes and their analysis in this setting. The spectral Galerkin method, that is, using trigonometric polynomials as basis is then discussed and we show its spectral accuracy. Finally the pseudo-spectral method is presented, its implementation via the DFT is discussed.
Keywords
- Type
- Chapter
- Information
- Classical Numerical AnalysisA Comprehensive Course, pp. 721 - 741Publisher: Cambridge University PressPrint publication year: 2022