Computational Conformal Mapping
Springer-Verlag New York Inc.
978-1-4612-7376-9 (ISBN)
Green'sfunctionsforsuchsimple regions are known. However, for regions with complex structure the solution ofa boundary value problem often becomes more difficult, even for a simple problemsuchastheDirichletproblem. Oneapproachtosolvingthesedifficult problems is to conformally transform a given multiply connected region onto *Mathematica is a registered trade mark of Wolfram Research, Inc. ix x PREFACE simpler canonical regions. This will, however, result in change not only in the region and the associated boundary conditions but also in the governing differential equation. As compared to the simply connected regions, confor- mal mapping ofmultiply connected regions suffers from severe limitations, one of which is the fact that equal connectivity ofregions is not a sufficient condition to effect a reciprocally connected map ofone region onto another.
0. Introduction.- 1. Basic Concepts.- 2. Conformal Mappings.- 3. Schwarz—Christoffel Integrals.- 4. Polynomial Approximations.- 5. Nearly Circular Regions.- 6. Green’s Functions.- 7. Integral Equation Methods.- 8. Theodorsen’s Integral Equation.- 9. Symm’s Integral Equation.- 10. Airfoils.- 11. Doubly Connected Regions.- 12. Singularities.- 13. Multiply Connected Regions.- 14. Grid Generation.- Appendix A. Cauchy P. V. Integrals.- A.1. Numerical Evaluation.- Appendix B. Green’s Identities.- Appendix C. Riemann—Hilbert Problem.- C.1. Homogeneous Hilbert Problem.- C.2. Nonhomogeneous Hilbert Problem.- C.3. Riemann—Hilbert Problem.- Appendix D. Successive Approximations.- D.1. Tables.- Appendix E. Catalog of Conformal Mappings.- Bibliography 431 Notation.
Zusatzinfo | XV, 462 p. |
---|---|
Verlagsort | New York |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 1-4612-7376-5 / 1461273765 |
ISBN-13 | 978-1-4612-7376-9 / 9781461273769 |
Zustand | Neuware |
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