Abstract
In part I, basic properties of a class of functions (called Psi-functions) are investigated, e.g., series representation, recurrence relation, asymptotic behavior. In part II, the solution of some versions of the diffusion equation by a series of Psi- and Omega-functions is treated. Psi-functions may be used as auxiliary functions in the case of one-dimensional non-stationary diffusion under removal process or forced convection.
Zusammenfassung
In Teil I werden grundlegende Eigenschaften einer Klasse von Funktionen (genannt Psi-Funktionen) untersucht, z.B. Reihenentwicklung, Rekursion, asymptotisches Verhalten. In Teil II wird die Lösung einiger Versionen der Diffusionsgleichung durch eine Reihe nach Psi- und Omega-Funktionen behandelt. Psi-Funktionen eignen sich als Hilfsfunktionen im Fall eindimensionaler nichtstationärer Diffusion bei Absorption oder erzwungener Konvektion.
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Kahlig, P. Further auxiliary functions for non-stationary one-dimensional diffusion. Part II: Applications. Journal of Applied Mathematics and Physics (ZAMP) 28, 1109–1119 (1977). https://doi.org/10.1007/BF01601677
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DOI: https://doi.org/10.1007/BF01601677