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Computational Partial Differential Equations

Numerical Methods and Diffpack Programming

  • Hans Petter Langtangen

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 1)

Table of contents

  1. Front Matter
    Pages I-XXVI
  2. Hans Petter Langtangen
    Pages 1-139
  3. Hans Petter Langtangen
    Pages 141-249
  4. Hans Petter Langtangen
    Pages 251-458
  5. Hans Petter Langtangen
    Pages 459-491
  6. Hans Petter Langtangen
    Pages 493-537
  7. Hans Petter Langtangen
    Pages 539-594
  8. Hans Petter Langtangen
    Pages 595-632
  9. Back Matter
    Pages 633-861

About this book

Introduction

The second edition features lots of improvements and new material. The most significant additions include - finite difference methods and implementations for a 1D time-dependent heat equation (Chapter 1. 7. 6), - a solver for vibration of elastic structures (Chapter 5. 1. 6), - a step-by-step instruction of how to develop and test Diffpack programs for a physical application (Chapters 3. 6 and 3. 13), - construction of non-trivial grids using super elements (Chapters 3. 5. 4, 3. 6. 4, and 3. 13. 4), - additional material on local mesh refinements (Chapter 3. 7), - coupling of Diffpack with other types of software (Appendix B. 3) - high-level programming offinite difference solvers utilizing the new stencil (finite difference operator) concept in Diffpack (Appendix D. 8). Many of the examples, projects, and exercises from the first edition have been revised and improved. Some new exercises and projects have also been added. A hopefully very useful new feature is the compact overview of all the program examples in the book and the associated software files, presented in Chapter 1. 2. Errors have been corrected, many explanations have been extended, and the text has been upgraded to be compatible with Diffpack version 4. 0. The major difficulty when developing programs for numerical solution of partial differential equations is to debug and verify the implementation. This requires an interplay between understanding the mathematical model,the in­ volved numerics, and the programming tools.

Keywords

C++ computer finite element method fluid mechanics mechanics model numerical methods numerics programming

Authors and affiliations

  • Hans Petter Langtangen
    • 1
    • 2
  1. 1.Simula Research LaboratoryLysakerNorway
  2. 2.Department of InformaticsUniversity of OsloOsloNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-55769-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-62811-5
  • Online ISBN 978-3-642-55769-9
  • Series Print ISSN 1611-0994
  • Buy this book on publisher's site