The Theory of Difference Schemes

by Alexander A. Samarskii

Overview

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques."

Product Details

ISBN-13:	9780824704681
Publisher:	Taylor & Francis
Publication date:	03/29/2001
Series:	Pure and Applied Mathematics Series , #240
Pages:	788
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Alexander A. Samarskii

Table of Contents

Preliminaries; basic concepts of the theory of difference schemes; homogeneous difference schemes; difference schemes for elliptic equations; different schemes for time-dependent equations with constant coefficients; stability theory of differenceschemes; symbols; concluding remarks.

Editorial Reviews

"Illustrated with helpful examples of practical implementations of general stability."
—ZDM: The International Journal on Mathematics Education

"…well written … delivers more than one may expect. … an excellent book, with a wealth of mathematical material and techniques."
—Mathematical Reviews

"…an extensive theoretical survey."
—Zentralblatt MATH

From the Publisher

..well written...delivers more than one may expect.... An excellent book, with a wealth of mathematical material and techniques.

Mathematical Reviews

Treats the theory of difference methods (schemes) applied to typical problems in mathematical physics. Summarizes basics such as stability, approximation, and convergence, then demonstrates applications of estimates for establishing convergence and expressing stability to two- and three-layer schemes with initial data. Describes homogeneous difference schemes in the class of discontinuous coefficients, and addresses difference schemes as operator and operator-difference equations without structural constraints and as nonstationary equations with constant coefficients. Samarskii is founder and director of the Institute of Mathematical Modeling of the Russian Academy of Sciences, and professor of computational mathematics at Moscow M. V. Lomonosov State University, Russia. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews