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

Nonfiction, Science & Nature, Mathematics, Differential Equations, Applied
Cover of the book Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings by Evgenii A. Volkov, CRC Press
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Author: Evgenii A. Volkov ISBN: 9781351367875
Publisher: CRC Press Publication: July 28, 2017
Imprint: CRC Press Language: English
Author: Evgenii A. Volkov
ISBN: 9781351367875
Publisher: CRC Press
Publication: July 28, 2017
Imprint: CRC Press
Language: English

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 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.

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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 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.

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