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The bulletin of mathematical biophysics

, Volume 15, Issue 1, pp 49–61 | Cite as

An approximation method for the solution of diffusion and related problems

  • H. D. Landahl
Article

Abstract

An approximation method is introduced which enables a number of diffusion-type problems to be solved in an approximate but simple manner. Many cases require only the solution of a simple first-order differential equation. The method is applied to a number of cases in which the exact solutions are available. A comparison shows that the method is quite satisfactory in these cases. The method is applied to diffusion problems with rate of consumption proportional to concentration or to the square of the concentration. In the latter case, the result obtained is essentially the same as that found by H. G. Landau (1950) after elaborate calculations.

Keywords

Approximation Method Relate Problem Biophysics Volume Simple Manner Mathematical Biophysics 
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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Literature

  1. Carslaw, H. S. 1945.The Mathematical Theory of the Conduction of Heat in Solids. Second Ed., completely revised. New York: Dover Publications.zbMATHGoogle Scholar
  2. Landau, H. G. 1950. “A Problem in Radiobiology: Diffusion and Recombination of Ions”.Bull. Math. Biophysics,12, 27–34.Google Scholar
  3. Rashevsky, N. 1948.Mathematical Biophysics. Rev. Ed., Chicago: University of Chicago Press.zbMATHGoogle Scholar

Copyright information

© The University of Chicago Press 1953

Authors and Affiliations

  • H. D. Landahl
    • 1
  1. 1.The University of ChicagoCommittee on Mathematical BiologyUSA

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