Appendix C. Legendre Functions and the Gaussian Quadrature

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xi
4. PART 1. The Fundamentals
5. Chapter One. A Model of Rayleigh-Bénard Convection 3
6. Chapter Two. Numerical Method 17
7. Chapter Three. Linear Stability Analysis 27
8. Chapter Four. Nonlinear Finite-Amplitude Dynamics 35
9. Chapter Five. Postprocessing 51
10. Chapter Six. Internal Gravity Waves 59
11. Chapter Seven. Double-Diffusive Convection 68
12. PART 2. Additional Numerical Methods
13. Chapter Eight. Time Integration Schemes 85
14. Chapter Nine. Spatial Discretizations 95
15. Chapter Ten. Boundaries and Geometries 115
16. PART 3. Additional Physics
17. Chapter Eleven. Magnetic Field 169
18. Chapter Twelve. Density Stratification 193
19. Chapter Thirteen. Rotation 229
20. Appendix A. A Tridiagonal Matrix Solver 283
21. Appendix B. Making Computer-Graphical Movies 284
22. Appendix C. Legendre Functions and the Gaussian Quadrature 288
23. Appendix D. Parallel Processing: OpenMP 291
24. Appendix E. Parallel Processing: MPI 292
25. Bibliography 295
26. Index 307