book chapter · Simula SpringerBriefs on computing · 2023

The Diffusion Equation

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Abstract

Abstract The diffusion equation appears in many applications in science and engineering, and computational physiology is no exception. In its most basic form, the diffusion equation is also useful as an example of how to deal with a PDE using numerical methods. We will start by considering it as a stand-alone model, but in the next chapterswe will study it in combination with non-linear ODEs. This chapter therefore serves as a warm-up for the more complex models. We will also follow the path we started above. In the very simplest case of an ODE, we found a formula for the solution of both the differential equation and the numerical scheme approximating the equation. One nice consequence of this is that, as we saw above, we can explicitly study the error introduced by the numerical approximation. In this chapter, we will use the same approach to study the error of the numerical approximation of the diffusion equation.

Cite this paper

APA 7

Jæger, K. H., & Tveito, A. (2023). The Diffusion Equation. Simula SpringerBriefs on computing, 21–32. https://doi.org/10.1007/978-3-031-30852-9_3

MLA 9

Jæger, Karoline Horgmo, and Aslak Tveito. “The Diffusion Equation.” Simula SpringerBriefs on computing, 2023, pp. 21–32, https://doi.org/10.1007/978-3-031-30852-9_3.

Chicago

Jæger, Karoline Horgmo, and Aslak Tveito. 2023. “The Diffusion Equation.” Simula SpringerBriefs on computing: 21–32. https://doi.org/10.1007/978-3-031-30852-9_3.

Harvard

Jæger, K.H. and Tveito, A. (2023) ‘The Diffusion Equation’, Simula SpringerBriefs on computing, pp. 21–32. Available at: https://doi.org/10.1007/978-3-031-30852-9_3.

BibTeX

@incollection{jger2023diffusion,
  title = {{The Diffusion Equation}},
  author = {Jæger, Karoline Horgmo and Tveito, Aslak},
  booktitle = {Simula SpringerBriefs on computing},
  pages = {21--32},
  year = {2023},
  doi = {10.1007/978-3-031-30852-9_3}
}

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