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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Differential calculus and equations > Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings
Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings

Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings


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About the Book

This book presents a new and efficient numerical analytical method for solving the Laplace equation on an arbitrary polygon called the approximate block method. The block method overcomes indicated difficulties naturally and has qualitatively more rapid convergence than well-known difference and variational-difference methods. The block method also solves the complicated problem of approximate conformal mapping of multiply-connected polygons onto canonical domains with no preliminary information required. The high precision results of calculations carried out on the computer are presented in an abundance of tables substantiating the exponential convergence of the block method and its strong stability concerning the rounding-off of errors.

Table of Contents:
Approximate Block Method for Solving the Laplace Equation on Polygons Setting up a Mixed Boundary Value Problem for the Laplace Equation on a Polygon A Finite Covering of a Polygon by Blocks of Three Types Representation of the Solution of a Boundary Value Problem on Blocks An Algebraic Problem The Main Result - Theorem on the Convergence of the Block Method Proofs of Theorem and Lemmas The Stability and the Labor Content of Computations Required by the Block Method Approximation of a Conjugate Harmonic Function on Blocks Neumann's Problem The Case of Arbitrary Analytic Mixed Boundary Conditions Approximate Block Method of Conformal Mapping of Polygons onto Canonical Domains Approximate Conformal Mapping of a Simply-Connected Polygon onto a Disk Basic Harmonic Functions Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Plane with Cuts along Parallel Line Segments Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Ring with Cuts along the Arcs of Concentric Circles Development and Application of the Approximate Block Method for Conformal Mapping of Simply-Connected and Doubly-Connected Domains Approximate Conformal Mapping of Some Polygons onto a Strip Scheme of Constructing a Conformal Mapping of a Doubly-connected Domain onto a Ring Mapping a Square Frame onto a Ring Mapping a Square with a Circular Hole Using Circular Lune Block Representation of a Harmonic Function on a Ring Using a Block-Ring for Mapping Domain (18.1) onto a Ring A Block-Bridge Limit Cases Mapping a Disk with an Elliptic Hole or with a Retro-Section onto a Ring Mapping a Disk with a Regular Polygonal Hole Mapping the Exterior of a Parabola with a Hole onto a Ring Approximate Conformal Mapping of Domains with a Periodic Structure by the Block Method Mapping a Domain of the Type of Half-Plane with a Periodic Structure onto a Half-plane Mapping a Domain of the Type of Strip with a Periodic Structure onto a Strip Mapping the Exterior of a Lattice of Ellipses onto the Exterior of a Lattice of Plates References Index


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Product Details
  • ISBN-13: 9780849394065
  • Publisher: Taylor & Francis Inc
  • Publisher Imprint: CRC Press Inc
  • Height: 235 mm
  • No of Pages: 240
  • Returnable: N
  • Width: 156 mm
  • ISBN-10: 0849394066
  • Publisher Date: 06 Jul 1994
  • Binding: Hardback
  • Language: English
  • No of Pages: 240
  • Weight: 408 gr


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Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings
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