Spline Collocation Methods for Partial Differential Equations ：With Applications in R

Publication subTitle ：With Applications in R

Author： William E. Schiesser  

Publisher： John Wiley & Sons Inc‎

Publication year： 2017

E-ISBN: 9781119301059

P-ISBN(Paperback): 9781119301035

Subject： O175.26 parabolic equation

Keyword： differential equations solving differential equations collocation analysis of partial differential equations how to solve differential equations methods of solving differential equations partial differential equations solving partial differential equations functional differential equations how to solve partial differential equations methods of solving partial differential equation numerical integration of partial differential equations methods of numerical integration of partial diffe

Language： ENG

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Chapter

Cover

Title Page

Copyright

Dedication

Contents

Preface

About the Companion Website

Chapter 1 Introduction

1.1 Uniform Grids

1.2 Variable Grids

1.3 Stagewise Differentiation

Appendix A1 - Online Documentation for splinefun

Reference

Chapter 2 One-Dimensional PDEs

2.1 Constant Coefficient

2.1.1 Dirichlet BCs

2.1.1.1 Main Program

2.1.1.2 ODE Routine

2.1.2 Neumann BCs

2.1.2.1 Main Program

2.1.2.2 ODE Routine

2.1.3 Robin BCs

2.1.3.1 Main Program

2.1.3.2 ODE Routine

2.1.4 Nonlinear BCs

2.1.4.1 Main Program

2.1.4.2 ODE Routine

2.2 Variable Coefficient

2.2.1 Main Program

2.2.2 ODE Routine

2.3 Inhomogeneous, Simultaneous, Nonlinear

2.3.1 Main Program

2.3.2 ODE routine

2.3.3 Subordinate Routines

2.4 First Order in Space and Time

2.4.1 Main Program

2.4.2 ODE Routine

2.4.3 Subordinate Routines

2.5 Second Order in Time

2.5.1 Main Program

2.5.2 ODE Routine

2.5.3 Subordinate Routine

2.6 Fourth Order in Space

2.6.1 First Order in Time

2.6.1.1 Main Program

2.6.1.2 ODE Routine

2.6.2 Second Order in Time

2.6.2.1 Main Program

2.6.2.2 ODE Routine

References

Chapter 3 Multidimensional PDEs

3.1 2D in Space

3.1.1 Main Program

3.1.2 ODE Routine

3.2 3D in Space

3.2.1 Main Program, Case 1

3.2.2 ODE Routine

3.2.3 Main Program, Case 2

3.2.4 ODE Routine

3.3 Summary and Conclusions

Chapter 4 Navier-Stokes, Burgers' Equations

4.1 PDE Model

4.2 Main Program

4.3 ODE Routine

4.4 Subordinate Routine

4.5 Model Output

4.6 Summary and Conclusions

Reference

Chapter 5 Korteweg-de Vries Equation

5.1 PDE Model

5.2 Main Program

5.3 ODE Routine

5.4 Subordinate Routines

5.5 Model Output

5.6 Summary and Conclusions

References

Chapter 6 Maxwell Equations

6.1 PDE Model

6.2 Main Program

6.3 ODE Routine

6.4 Model Output

6.5 Summary and Conclusions

Appendix A6.1. Derivation of the Analytical Solution

Reference

Chapter 7 Poisson-Nernst-Planck Equations

7.1 PDE Model

7.2 Main Program

7.3 ODE Routine

7.4 Model Output

7.5 Summary and Conclusions

References

Chapter 8 Fokker-Planck Equation

8.1 PDE Model

8.2 Main Program

8.3 ODE Routine

8.4 Model Output

8.5 Summary and Conclusions

References

Chapter 9 Fisher-Kolmogorov Equation

9.1 PDE Model

9.2 Main Program

9.3 ODE Routine

9.4 Subordinate Routine

9.5 Model Output

9.6 Summary and Conclusions

Reference

Chapter 10 Klein-Gordon Equation

10.1 PDE Model, Linear Case

10.2 Main Program

10.3 ODE Routine

10.4 Model Output

10.5 PDE Model, Nonlinear Case

10.6 Main Program

10.7 ODE Routine

10.8 Subordinate Routines

10.9 Model Output

10.10 Summary and Conclusions

Reference

Chapter 11 Boussinesq Equation

11.1 PDE Model

11.2 Main Program

11.3 ODE Routine

11.4 Subordinate Routines

11.5 Model Output

11.6 Summary and Conclusions

References

Chapter 12 Cahn-Hilliard Equation

12.1 PDE Model

12.2 Main Program

12.3 ODE Routine

12.4 Model Output

12.5 Summary and Conclusions

References

Chapter 13 Camassa-Holm Equation

13.1 PDE Model

13.2 Main Program

13.3 ODE Routine

13.4 Model Output

13.5 Summary and Conclusions

13.6 Appendix A13.1: Second Example of a PDE with a Mixed Partial Derivative

13.7 Main Program

13.8 ODE Routine

13.9 Model Output

Reference

Chapter 14 Burgers-Huxley Equation

14.1 PDE Model

14.2 Main Program

14.3 ODE Routine

14.4 Subordinate Routine

14.5 Model Output

14.6 Summary and Conclusions

References

Chapter 15 Gierer-Meinhardt Equations

15.1 PDE Model

15.2 Main Program

15.3 ODE Routine

15.4 Model Output

15.5 Summary and Conclusions

Reference

Chapter 16 Keller-Segel Equations

16.1 PDE Model

16.2 Main Program

16.3 ODE Routine

16.4 Subordinate Routines

16.5 Model Output

16.6 Summary and Conclusions

Appendix A16.1. Diffusion Models

References

Chapter 17 Fitzhugh-Nagumo Equations

17.1 PDE Model

17.2 Main Program

17.3 ODE Routine

17.4 Model Output

17.5 Summary and Conclusions

Reference

Chapter 18 Euler-Poisson-Darboux Equation

18.1 PDE Model

18.2 Main Program

18.3 ODE Routine

18.4 Model Output

18.5 Summary and Conclusions

References

Chapter 19 Kuramoto-Sivashinsky Equation

19.1 PDE Model

19.2 Main Program

19.3 ODE Routine

19.4 Subordinate Routines

19.5 Model Output

19.6 Summary and Conclusions

References

Chapter 20 Einstein-Maxwell Equations

20.1 PDE Model

20.2 Main Program

20.3 ODE Routine

20.4 Model Output

20.5 Summary and Conclusions

Reference

Appendix A Differential Operators in Three Orthogonal Coordinate Systems

References

Index

EULA

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