2008 / xiv + 395 pages / Softcover / ISBN 978-0898716-52-8 / List Price $87.00 / SIAM Member Price $60.90 / Order Code CS05
Keywords: numerical algorithm, differential equation, time dependent problem, stability
Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applicaÂtions such as ﬂuid ﬂow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical ﬁnance.
This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well.
The author bridges theory and practice by developing algorithms, concepts, and analysis from basic principles while discussing efficiency and performance issues and demonstrating methods through examples and case studies from numerous application areas.
This textbook is suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Gradute students at the beginning or advanced level (depending on the discipline) and researchers in a variety of fields in science and engineering will find this book useful. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.
About the Author
Uri M. Ascher is a Professor of Computer Science at the University of British Columbia in Vancouver, Canada. He has previously co-authored two other books published by SIAM as well as many research papers in the general area of numerical methods for differential equations and their applications.
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