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Analysis of the Diffusion Equation

  • Aslak TveitoEmail author
  • Hans Petter Langtangen
  • Bjørn Frederik Nielsen
  • Xing Cai
Chapter
Part of the Texts in Computational Science and Engineering book series (TCSE, volume 7)

Abstract

In Chap. 7 we studied several aspects of the theory of diffusion processes. We saw how these equations arise in models of several physical phenomena and how they can be approximately solved by suitable numerical methods. The analysis of diffusion equations is a classic subject of applied mathematics and of scientific computing. Its impact on the field of partial differential equations (PDEs) has been very important, both from a theoretical and practical point of view. The purpose of this chapter is to dive somewhat deeper into this field and thereby increase our understanding of this important topic.

Keywords

Fourier Series Diffusion Equation Formal Solution Model Problem Smooth Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Aslak Tveito
    • 1
    • 2
    Email author
  • Hans Petter Langtangen
    • 1
    • 2
  • Bjørn Frederik Nielsen
    • 1
    • 3
  • Xing Cai
    • 1
    • 2
  1. 1.Center for Biomedical ComputingSimula Research LaboratoryLysakerNorway
  2. 2.Department of InformaticsUniversity of OsloOsloNorway
  3. 3.Department of Mathematical Sciences and TechnologyNorwegian University of Life SciencesÅsNorway

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