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Ch. 1 | Approximate Block Method for Solving the Laplace Equation on Polygons | 1 |
1 | Setting up a Mixed Boundary-Value Problem for the Laplace Equation on a Polygon | 1 |
2 | A Finite Covering of a Polygon by Blocks of Three Types | 13 |
3 | Representation of the Solution of a Boundary-Value Problem on Blocks | 19 |
4 | An Algebraic Problem | 34 |
5 | The Main Result | 40 |
6 | Proofs of Theorem 5.1 and of Lemmas 4.1-4.4 | 48 |
7 | The Stability and the Labor Content of Computations Required by the Block Method | 73 |
8 | Approximation of a Conjugate Harmonic Function on Blocks | 85 |
9 | Neumann's Problem | 92 |
10 | The Case of Arbitrary Analytic Mixed Boundary Conditions | 98 |
Ch. 2 | Approximate Block Method of Conformal Mapping of Polygons onto Canonical Domains | 108 |
11 | Approximate Conformal Mapping of a Simply-Connected Polygon onto a Disk | 108 |
12 | Basic Harmonic Functions | 111 |
13 | Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Plane with Cuts along Parallel Line Segments | 113 |
14 | Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Ring with Cuts along the Arcs of Concentric Circles | 119 |
Ch. 3 | Development and Application of the Approximate Block Method for Conformal Mapping of Simply-Connected and Doubly-Connected Domains | 124 |
15 | Approximate Conformal Mapping of Some Polygons onto a Strip | 124 |
16 | Scheme of Constructing a Conformal Mapping of a Doubly-Connected Domain onto a Ring | 141 |
17 | Mapping a Square Frame onto a Ring | 143 |
18 | Mapping a Square with a Circular Hole Using Circular Lune Block | 149 |
19 | Representation of a Harmonic Function on a Ring | 155 |
20 | Using a Block-Ring for Mapping Domain (18.1) onto a Ring | 157 |
21 | A Block-Bridge | 161 |
22 | Limit Cases | 167 |
23 | Mapping a Disk with an Elliptic Hole or with a Retrosection onto a Ring | 169 |
24 | Mapping a Disk with a Regular Polygonal Hole | 173 |
25 | Mapping the Exterior of a Parabola with a Hole onto a Ring | 181 |
Ch. 4 | Approximate Conformal Mapping of Domains with a Periodic Structure by the Block Method | 188 |
26 | Mapping a Domain of the Type of Half-Plane with a Periodic Structure onto a Half-Plane | 188 |
27 | Mapping a Domain of the Type of Strip with a Periodic Structure onto a Strip | 202 |
28 | Mapping the Exterior of a Lattice of Ellipses onto the Exterior of a Lattice of Plates | 210 |
References | 220 | |
Index | 225 |
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Add Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings, This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon. This method, called the approximate block method, overcomes indicated difficulties and has qualitatively more rapid convergence than , Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings to the inventory that you are selling on WonderClubX
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Add Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings, This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon. This method, called the approximate block method, overcomes indicated difficulties and has qualitatively more rapid convergence than , Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings to your collection on WonderClub |