Abstract
A class of problems in a generalized formulation is studied for the case of a half-strip. A theorem is proven on the existence and uniqueness of the solution in a weighted Sobolev space; a difference scheme is constructed on a finite lattice and the rate of its convergence is established.
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I. P. Gavrilyuk and V. L. Makarov, “A difference scheme on a finite lattice for a nonlinear parabolic equation on an unbounded domain,” Dokl. Akad, Nauk Ukr SSR, Ser. A, No. 7, 3–5 (1983)
I. P. Gavrilyuk and V. L. Makarov, “Difference schemes on the lattice space L2 for a class of problems with nonlinear boundary conditions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 31–38 (1985).
I. P. Gavrilyuk, V. L. Makarov, and T. L. Shmanenko, “The regularization of difference schemes for quasilinear elliptic equations in a strip,” Vychisl. Prikl. Mat., No. 39, 94–101 (1979).
V. L. Makarov and S. G. Gocheva, “Difference schemes of arbitrary order of precision for second-order differential equations on a half-axis,” Differents. Uravn.,17, No. 3, 527–540 (1981).
V. L. Makarov and A. A. Samarskii, “Application of exact difference schemes to the estimates of the rate of convergence of the tangent method,” Zh. Vychisl. Mat. Mat. Fiz.,20, No. 2, 371–387 (1980).
P. G. Ciarlet, The Finite-Element Method for Elliptic Problems, Elsevier Amsterdam (1978).
I. Babuska, “The finite-element method for infinite domains. I,” Math. Computation,26, No. 117, 1–11 (1972).
G. Fix and G. Strang, “Fourier analysis of the finite-element method in Ritz-Galerkin theory,” Studies Appl. Math.,48, 265–273 (1969).
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Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 28–37, 1989.
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Gavrilyuk, I.P., Makarov, L.V. A difference method for the solution of a class of generalized boundary-value problems in a half-strip. J Math Sci 67, 3052–3058 (1993). https://doi.org/10.1007/BF01098139
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DOI: https://doi.org/10.1007/BF01098139