Aec Research and Development Report: The Iterative Solution of Elliptic Difference Equations, June 1, 1957 (Classic Reprint) - Hardcover

Bernard Friedman

Hardcover

ISBN 10: 0656021276 ISBN 13: 9780656021277

Publisher: Forgotten Books, 2018

Synopsis

Understand how to solve elliptic difference equations more efficiently with proven iteration methods.

This guide explains why some iterative schemes converge faster and how their performance depends on matrix eigenvalues and problem structure.

Two main ideas frame the discussion. First, you replace a continuous boundary-value problem with a finite collection of algebraic equations and study how different iteration schemes approach the solution. Second, you compare methods that update all unknowns at once with those that update them in sequence, showing how order and grouping affect convergence.

• Learn how three-block schemes model coupling between parts of a system and how this structure influences speed.
• See how the rate of convergence relates to eigenvalues and determinant conditions, with practical criteria for choosing an algorithm.
• Compare simultaneous and successive displacements, and understand why the latter can converge faster in certain layouts.
• Explore how elliptic difference equations arise from discretizing boundary-value problems and how to form their matrix representations.

Ideal for readers of engineering, numerical analysis, and applied mathematics who want a solid, grounded view of iterative methods for elliptic problems.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0656021276
• ISBN 13: 9780656021277
• Binding: Hardcover
• Number of pages: 47