Preface; Introduction; 1. Evolution equations on the half-line; 2. Evolution equations on the finite interval; 3. Asymptotics and a novel numerical technique; 4. From PDEs to classical transforms; 5. Riemannndash;Hilbert and d-Bar problems; 6. The Fourier transform and its variations; 7. The inversion of the attenuated Radon transform and medical imaging; 8. The Dirichlet to Neumann map for a moving boundary; 9. Divergence formulation, the global relation, and Lax pairs; 10. Rederivation of the integral representations on the half-line and the finite interval; 11. The basic elliptic PDEs in a polygonal domain; 12. The new transform method for elliptic PDEs in simple polygonal domains; 13. Formulation of Riemannndash;Hilbert problems; 14. A collocation method in the Fourier plane; 15. From linear to integrable nonlinear PDEs; 16. Nonlinear integrable PDEs on the half-line; 17. Linearizable boundary conditions; 18. The generalized Dirichlet to Neumann map; 19. Asymptotics of oscillatory Riemannndash;Hilbert problems; Epilogue; Bibliography; Index.
| Introduction | p. 1 |
| A New Transform Method for Linear Evolution Equations | p. 35 |
| Evolution Equations on the Half-Line | p. 37 |
| Evolution Equations on the Finite Interval | p. 63 |
| Asymptotics and a Novel Numerical Technique | p. 77 |
| Analytical Inversion of Integrals | p. 85 |
| From PDEs to Classical Transforms | p. 87 |
| Riemann-Hilbert and d-Bar Problems | p. 91 |
| The Fourier Transform and Its Variations | p. 97 |
| The Inversion of the Attenuated Radon Transform and Medical Imaging | p. 103 |
| The Dirichlet to Neumann Map for a Moving Boundary | p. 113 |
| Novel Integral Representations for Linear Boundary Value Problems | p. 125 |
| Divergence Formulation, the Global Relation, and Lax Pairs | p. 129 |
| Rederivation of the Integral Representations on the Half-Line and the Finite Interval | p. 137 |
| The Basic Elliptic PDEs in a Polygonal Domain | p. 141 |
| Novel Analytical and Numerical Methods for Elliptic PDEs in a Convex Polygon | p. 159 |
| The New Transform Method for Elliptic PDEs in Simple Polygonal Domains | p. 163 |
| Formulation of Riemann-Hilbert Problems | p. 189 |
| A Collocation Method in the Fourier Plane | p. 195 |
| Integrable Nonlinear PDEs | p. 213 |
| From Linear to Integrable Nonlinear PDEs | p. 217 |
| Nonlinear Integrable PDEs on the Half-Line | p. 225 |
| Linearizable Boundary Conditions | p. 271 |
| The Generalized Dirichlet to Neumann Map | p. 283 |
| Asymptotics of Oscillatory Riemann-Hilbert Problems | p. 301 |
| Epilogue | p. 315 |
| Bibliography | p. 321 |
| Index | p. 335 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
ISBN: 9780898716511
ISBN-10: 0898716519
Publisher:
Society for Industrial & Applied Mathematics
Format:
Paperback
Language:
English
Dimensions (cm): 25.000 x 17.100
x 1.500
Weight (kg): 0.560
Audience:
Tertiary; University or College
Click to Enlarge
