Abstract
(1) ONE of the most valuable methods for the approximate solution of the differential equations of mathematical physics is that due to Lord Rayleigh and W. Ritz. This starts by applying the calculus of variations to a certain quadratic form and finally obtains a solution in terms of a convergent series of functions; a limited number of terms of this series gives an approximation to the exact solution. However, the method as left by its authors was not fully developed, and a great deal of work has been done by Prof. Kryloff, who has written more than thirty papers on the subject. An essential part of his contributions is to show how to estimate the number of terms which must be taken to make the error less than an arbitrary assigned amount.
(1) Les méthodes de solution approchée des problèmes dela physique mathématique.
Par Nicolas Kryloff. (Mémorial des sciences mathématiques, Fascicule 49.) Pp. 69. (Paris: Gauthier-Villars et Cie, 1931.) 15 francs.
(2) Angenäherte und symbolische Lösung der Differentialgleichungen der mathematischen Physik und Technik.
Von Prof. Dr. N. M. Kryloff. Pp. 162. (Kharkov and Kiev: State Technical Publishers, 1931.) 3 Kps.
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H. P., H. Mathematics. Nature 128, 963 (1931). https://doi.org/10.1038/128963a0
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DOI: https://doi.org/10.1038/128963a0