Block method for solving the Laplace equation and for constructing conformal mappings / E.A. Volkov

Includes bibliographical references (pages 220-224) and index

Ch. 1. Approximate Block Method for Solving the Laplace Equation on Polygons. 1. Setting up a Mixed Boundary-Value Problem for the Laplace Equation on a Polygon. 2. A Finite Covering of a Polygon by Blocks of Three Types. 3. Representation of the Solution of a Boundary-Value Problem on Blocks. 4. An Algebraic Problem. 5. The Main Result. 6. Proofs of Theorem 5.1 and of Lemmas 4.1-4.4. 7. The Stability and the Labor Content of Computations Required by the Block Method. 8. Approximation of a Conjugate Harmonic Function on Blocks. 9. Neumann's Problem. 10. The Case of Arbitrary Analytic Mixed Boundary Conditions -- Ch. 2. Approximate Block Method of Conformal Mapping of Polygons onto Canonical Domains. 11. Approximate Conformal Mapping of a Simply-Connected Polygon onto a Disk. 12. Basic Harmonic Functions. 13. Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Plane with Cuts along Parallel Line Segments

14. Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Ring with Cuts along the Arcs of Concentric Circles -- Ch. 3. Development and Application of the Approximate Block Method for Conformal Mapping of Simply-Connected and Doubly-Connected Domains. 15. Approximate Conformal Mapping of Some Polygons onto a Strip. 16. Scheme of Constructing a Conformal Mapping of a Doubly-Connected Domain onto a Ring. 17. Mapping a Square Frame onto a Ring. 18. Mapping a Square with a Circular Hole Using Circular Lune Block. 19. Representation of a Harmonic Function on a Ring. 20. Using a Block-Ring for Mapping Domain (18.1) onto a Ring. 21. A Block-Bridge. 22. Limit Cases. 23. Mapping a Disk with an Elliptic Hole or with a Retrosection onto a Ring. 24. Mapping a Disk with a Regular Polygonal Hole. 25. Mapping the Exterior of a Parabola with a Hole onto a Ring -- Ch. 4. Approximate Conformal Mapping of Domains with a Periodic Structure by the Block Method

26. Mapping a Domain of the Type of Half-Plane with a Periodic Structure onto a Half-Plane. 27. Mapping a Domain of the Type of Strip with a Periodic Structure onto a Strip. 28. Mapping the Exterior of a Lattice of Ellipses onto the Exterior of a Lattice of Plates