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.
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Literature
Carslaw, H. S. 1945.The Mathematical Theory of the Conduction of Heat in Solids. Second Ed., completely revised. New York: Dover Publications.
Landau, H. G. 1950. “A Problem in Radiobiology: Diffusion and Recombination of Ions”.Bull. Math. Biophysics,12, 27–34.
Rashevsky, N. 1948.Mathematical Biophysics. Rev. Ed., Chicago: University of Chicago Press.
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Landahl, H.D. An approximation method for the solution of diffusion and related problems. Bulletin of Mathematical Biophysics 15, 49–61 (1953). https://doi.org/10.1007/BF02476367
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DOI: https://doi.org/10.1007/BF02476367