An application of the method of moments to stochastic equations
Author:
John J. McCoy
Journal:
Quart. Appl. Math. 26 (1969), 521-536
MSC:
Primary 60.75
DOI:
https://doi.org/10.1090/qam/235629
MathSciNet review:
235629
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Abstract: A modified form of Galerkin's method is formally applied to an equation involving a stochastic bounded linear operator. The result, in general, is a sequence of stochastic linear algebraic equations. In the case of a statistically homogeneous operator, however, it is possible to obtain a sequence of deterministic linear algebraic equations. The formalism is applied to determining the electric field in a dielectric with a statistically homogeneous random permittivity.
- [1] B. G. Galerkin, Vestnik Inzhenerov 1, 897 (1915)
- [2] M. V. Keldyš, Izv. Akad. Nauk SSSR Ser. Mat. 6, 309, (1942) (Russian)
- [3] L. V. Kantorovič, Uspehi Mat. Nauk. 3 No. 6. 89. (1948) (Russian)
- [4] S. G. Mihlin, Direct methods in mathematical physics, GITTL, Moscow, 1948 (Russian)
- [5] N. I. Polśkiľ, Dokl. Akad. Nauk SSSR 86, 469 (1952) (Russian)
- [6] M. A. Krasnoselśkiľ, Topological methods in the theory of non-linear integral equations, GITTL, Moscow, 1956 (Russian)
- [7] Ju. V. Vorobev, Method of moments in applied mathematics, translated from the Russian by B. Seckler, Gordon & Breach, New York, 1965 MR 0184400
- [8] S. Prager, J. Chem. Phys. 33, 122 (1960) MR 0112311
- [9] W. F. Brown, J. Chem. Phys. 23, 1514 (1955)
- [10] M. Beran and J. Molyneux, Nuovo Cimento (10) 30, 1406 (1963) MR 0164422
- [11] M. Beran, Nuovo Cimento (10) 38, 777 (1965)
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Additional Information
DOI:
https://doi.org/10.1090/qam/235629
Article copyright:
© Copyright 1969
American Mathematical Society