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Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This text develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified view. The author emphasises 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 non-smooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is also included. 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.

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Book Details

ISBN: 9780898716528
ISBN-10: 0898716527
Format: Paperback
(247mm x 174mm x 18mm)
Pages: 410
Imprint: Society for Industrial & Applied Mathematics,U.S.
Publisher: Society for Industrial & Applied Mathematics,U.S.
Publish Date: 4-Sep-2008
Country of Publication: United States


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Author Biography - Uri M. Ascher

Uri M. Ascher is a Professor of Computer Science at the University of British Columbia, Vancouver.