Difference Schemes With High Order of Accuracy for Solving Hyperbolic Equations (Classic Reprint) - Hardcover

Peter D. Lax

Hardcover

ISBN 10: 0267975171 ISBN 13: 9780267975174

Publisher: Forgotten Books, 2018

Synopsis

High-Order Difference Schemes for Hyperbolic Equations

A rigorous look at how to build stable, accurate time-stepping methods for hyperbolic systems. This work explains when a scheme stays bounded and how to achieve high order accuracy in time and space.

This edition focuses on the theory behind stability and accuracy, including practical criteria for selecting parameters, and the geometric interpretation of stability. It covers both linear and nonlinear systems, and shows how to extend methods to conservation laws and applications in compressible flow and magnetohydrodynamics. The text combines analysis with concrete scheme construction, offering a pathway from abstract conditions to implementable algorithms.

• How stability relates to the amplification matrix and its spectrum.
• Conditions that guarantee a given scheme achieves second-order or higher accuracy.
• The role of artificial viscosity in stabilizing schemes and extending their usable range.
• How to adapt schemes to variable coefficients and nonlinear conservation laws.

Ideal for readers of advanced numerical analysis and computational fluid dynamics who want a solid, math–driven foundation for designing stable, accurate schemes for hyperbolic problems.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0267975171
• ISBN 13: 9780267975174
• Binding: Hardcover
• Number of pages: 61