Revival: Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings (1994)

ISBN-13: 9781138557796 / Angielski / Miękka / 2019 / 238 str.

Evgenii A. Volkov

Opis

This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon.

Spis treści

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

O autorze

Evgenii A. Volkov is a professor at the Steklov Mathematical Institute in Moscow, Russia.