Abstract
We consider the application of the fictitious region method to solve one class of nonlinear boundary-value problems with nonlinearity only in the boundary condition. A rate of convergence bound is obtained.
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O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1975).
S. A. Voitsekhovskii, “Fictitious region method for quasilinear equations of fourth-order,” Vychisl. Prikl. Mat., No. 51, 42–50 (1983).
H. Gajewski K. Gröger, and K. Zacharias, Nonlinear Operator Equations and Operator Differential Equations [Russian translation], Mir, Moscow (1978).
O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).
V. G. Osmolovskii and V. Ya. Rivkin, “Fictitious regoin method for the metal creep problem,” Chisl. Metody Mekh. Splosh. Sredy,8, No. 2, 89–94 (1977).
L. N. Slobodetskii, “Generalized Sobolev spaces and their application to boundary-value problems for partial differential equations,” Uch. Zapiski Leningr. Pedagog. Inst.,197, 54–112 (1958).
Sh. Smagulov, “Fictitious region method for the boundary-value problem of Navier-Stokes equations,” Preprint No. 68, VTs AN SSSR, Novosibirsk (1979).
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 16–19, 1986.
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Voitsekhovskii, S.A. Fictitious region method for one class of nonlinear boundary-value problems. J Math Sci 58, 401–404 (1992). https://doi.org/10.1007/BF01100063
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DOI: https://doi.org/10.1007/BF01100063