Computational Partial Differential Equations

Numerical Methods and Diffpack Programming

  • Hans Petter Langtangen

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 2)

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Hans Petter Langtangen
    Pages 1-108
  3. Hans Petter Langtangen
    Pages 109-211
  4. Hans Petter Langtangen
    Pages 213-334
  5. Hans Petter Langtangen
    Pages 335-366
  6. Hans Petter Langtangen
    Pages 367-401
  7. Hans Petter Langtangen
    Pages 403-456
  8. Hans Petter Langtangen
    Pages 457-490
  9. Back Matter
    Pages 491-685

About this book

Introduction

During the last decades there has been a tremendous advancement of com­ puter hardware, numerical algorithms, and scientific software. Engineers and scientists are now equipped with tools that make it possible to explore real­ world applications of high complexity by means of mathematical models and computer simulation. Experimentation based on numerical simulation has become fundamental in engineering and many of the traditional sciences. A common feature of mathematical models in physics, geology, astrophysics, mechanics, geophysics, as weH as in most engineering disciplines, is the ap­ pearance of systems of partial differential equations (PDEs). This text aims at equipping the reader with tools and skills for formulating solution methods for PDEs and producing associated running code. Successful problem solving by means of mathematical models inscience and engineering often demands a synthesis of knowledge from several fields. Besides the physical application itself, one must master the tools of math­ ematical modeling, numerical methods, as weH as software design and im­ plementation. In addition, physical experiments or field measurements might play an important role in the derivation and the validation of models. This book is written in the spirit of computational sciences as inter-disciplinary activities. Although it would be attractive to integrate subjects like mathe­ matics, physics, numerics, and software in book form, few readers would have the necessary broad background to approach such a text.

Keywords

Approximation C++ programming language Derivative Windows algorithm algorithms calculus differential equation finite elements mathematics numerics object-oriented programming programming simulation verification

Authors and affiliations

  • Hans Petter Langtangen
    • 1
  1. 1.Mechanics Division, Department of MathematicsUniversity of OsloOsloNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-01170-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-01172-0
  • Online ISBN 978-3-662-01170-6
  • Series Print ISSN 1439-7358
  • About this book
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