Book contents
- Frontmatter
- Contents
- Preface
- 1 An Introduction to the Method of Lines
- 2 A One-Dimensional, Linear Partial Differential Equation
- 3 Green's Function Analysis
- 4 Two Nonlinear, Variable-Coefficient, Inhomogeneous Partial Differential Equations
- 5 Euler, Navier Stokes, and Burgers Equations
- 6 The Cubic Schrödinger Equation
- 7 The Korteweg–deVries Equation
- 8 The Linear Wave Equation
- 9 Maxwell's Equations
- 10 Elliptic Partial Differential Equations: Laplace's Equation
- 11 Three-Dimensional Partial Differential Equation
- 12 Partial Differential Equation with a Mixed Partial Derivative
- 13 Simultaneous, Nonlinear, Two-Dimensional Partial Differential Equations in Cylindrical Coordinates
- 14 Diffusion Equation in Spherical Coordinates
- Appendix 1 Partial Differential Equations from Conservation Principles: The Anisotropic Diffusion Equation
- Appendix 2 Order Conditions for Finite-Difference Approximations
- Appendix 3 Analytical Solution of Nonlinear, Traveling Wave Partial Differential Equations
- Appendix 4 Implementation of Time-Varying Boundary Conditions
- Appendix 5 The Differentiation in Space Subroutines Library
- Appendix 6 Animating Simulation Results
- Index
- Plate section
5 - Euler, Navier Stokes, and Burgers Equations
Published online by Cambridge University Press: 08 October 2009
- Frontmatter
- Contents
- Preface
- 1 An Introduction to the Method of Lines
- 2 A One-Dimensional, Linear Partial Differential Equation
- 3 Green's Function Analysis
- 4 Two Nonlinear, Variable-Coefficient, Inhomogeneous Partial Differential Equations
- 5 Euler, Navier Stokes, and Burgers Equations
- 6 The Cubic Schrödinger Equation
- 7 The Korteweg–deVries Equation
- 8 The Linear Wave Equation
- 9 Maxwell's Equations
- 10 Elliptic Partial Differential Equations: Laplace's Equation
- 11 Three-Dimensional Partial Differential Equation
- 12 Partial Differential Equation with a Mixed Partial Derivative
- 13 Simultaneous, Nonlinear, Two-Dimensional Partial Differential Equations in Cylindrical Coordinates
- 14 Diffusion Equation in Spherical Coordinates
- Appendix 1 Partial Differential Equations from Conservation Principles: The Anisotropic Diffusion Equation
- Appendix 2 Order Conditions for Finite-Difference Approximations
- Appendix 3 Analytical Solution of Nonlinear, Traveling Wave Partial Differential Equations
- Appendix 4 Implementation of Time-Varying Boundary Conditions
- Appendix 5 The Differentiation in Space Subroutines Library
- Appendix 6 Animating Simulation Results
- Index
- Plate section
Summary
- Type
- Chapter
- Information
- A Compendium of Partial Differential Equation ModelsMethod of Lines Analysis with Matlab, pp. 90 - 113Publisher: Cambridge University PressPrint publication year: 2009