Presenting the block method-a new way to solve boundary-value problems for the Laplace equation

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

Author - Evgenii A. Volkov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

DESCRIPTION

This book presents a new, efficient numerical-analytical method for solving t he Laplace equation on an arbitrary polygon called the approximate block method. The block method overcomes indicated difficulties naturally and has qualitative ly more rapid convergence than well-known difference and variational-difference methods. The block method also solves the complicated problem of approximate con formal mapping of multiply-connected polygons onto canonical domains with no pre liminary information required. The high-precision results of calculations carrie d 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.

AUDIENCE

Researchers, practitioners, post-graduates, and all who routinely work with a pproximate methods of solving differential equations.

CONTENTS

• Approximate Block Method for Solving the Laplace Equation on Polygons
• Approximate Block Method of Conformal Mapping of Polygons onto Canonical Dom ains
• Development and Application of the Approximate Block Method for Conformal Ma pping of Simply-Connected and Doubly-Connected Domains
• Approximate Conformal Mapping of Domains with a Periodic Structure by the Bl ock Method
• References
• Index.

Catalog no. 9406

July 1994, 240 pp., ISBN: 0-8493-9406-6

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