Abstract
We consider the application of the fictitious region method to solve the first and second boundary-value problems for a second-order quasilinear elliptical equation. Rate of convergence bounds are obtained for two versions of the fictitious region method.
Similar content being viewed by others
Literature cited
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, “Method of fictitious regions for fourth-order quasilinear equations,” Vychisl. Prikl. Mat., No. 51, 42–50 (1983).
H. Gajewski, K. Groeger, and K. Zacharias, Nonlinear Operator Equations and Operator Differential Equations [Russian translation], Mir, Moscow (1978).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptical Equations [in Russian], Nauka, Moscow (1973).
L. N. Slobodetskii, “Generalized Sobolev spaces and their application to boundary-value problems for partial differential equations,” Uch. Zap. Leningrad. Gos. Ped. Inst.,197, 54–112 (1958).
Author information
Authors and Affiliations
Additional information
Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 7–14, 1985
Rights and permissions
About this article
Cite this article
Voitsekhovskii, S.A. Method of fictitious regions for second-order quasilinear elliptical equations. J Math Sci 54, 751–757 (1991). https://doi.org/10.1007/BF01097582
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01097582