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  • Textbook
  • Open Access
  • © 2017

Finite Difference Computing with PDEs

A Modern Software Approach

  • An easy-to-read text explaining the ideas behind finite

  • Uses fundamental PDEs to illustrate the path from algorithm to well-designed, complete computer code

  • Explains and demonstrates the skill of verifying computer code on the basis of numerous examples

  • Elaborates on artifacts in simulation results, further enhancing readers’ understanding

  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 16)

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (5 chapters)

  1. Front Matter

    Pages i-xxiii
  2. Vibration ODEs

    • Svein Linge, Hans Petter Langtangen
    Pages 1-92Open Access
  3. Wave Equations

    • Svein Linge, Hans Petter Langtangen
    Pages 93-205Open Access
  4. Diffusion Equations

    • Svein Linge, Hans Petter Langtangen
    Pages 207-322Open Access
  5. Advection-Dominated Equations

    • Svein Linge, Hans Petter Langtangen
    Pages 323-351Open Access
  6. Nonlinear Problems

    • Svein Linge, Hans Petter Langtangen
    Pages 353-407Open Access
  7. Back Matter

    Pages 409-507

About this book

This book is open access under a CC BY 4.0 license.

This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.


Keywords

  • Finite difference methods
  • Programming
  • Python
  • Verification
  • Numerical methods
  • Differential equations
  • Open access

Authors and Affiliations

  • Simula Research Laboratory , Lysaker, Norway

    Hans Petter Langtangen

  • Process,Energy&Environmental Technology, University College of Southeast Norway, Porsgrunn, Norway

    Svein Linge

About the authors

Svein Linge is a professor of modelling and simulation at the University College of Southeast Norway and holds a Dr. Scient. degree in biomechanics from the Norwegian School of Sport Sciences. He works part-time at a Norwegian Center of Excellence: "Center for Biomedical Computing", at Simula Research Laboratory, to which he has been linked for the last 13 years. His main research interests includes cerebrospinal fluid dynamics, cardiac electro-mechanics and sport biomechanics. Over the last decade, Linge has been particularly engaged in reforming the engineering education in mathematics and physics to take advantage of computer programming and simulation.

Hans Petter Langtangen was a professor of computer science at the University of Oslo. He had formerly been a professor of mechanics and was the director of a Norwegian Center of Excellence: "Center for Biomedical Computing", at Simula Research Laboratory. Langtangen published over 100 scientific publications and written several books, including papers and the bestseller TCSE 6 "A Primer on Scientific Programming with Python", now in its 5th edition. He also developed open source and commercial software systems for computational sciences. Hans Petter Langtangen passed away in October 2016.

 

Bibliographic Information

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)