Literature Cited
A. V. Bitsadze and A. A. Samarskii, “Simplest generalizations of linear elliptic boundary problems,” Dokl. Akad. Nauk SSSR,185, No. 4, 739–740 (1969).
R. Smith, Semiconductors [Russian translation], Mir, Moscow (1982).
E. Doolan, D. Miller, W. Shilders, Uniform Numerical Methods of Solution of Problems with a Boundary Layer [Russian translation], Mir, Moscow (1983).
A. E. Berger, J. M. Solomon, and M. Ciment, “An analysis of a uniformly accurate difference method for a singular perturbation problem,” Math. Comput.,37, 79–94 (1981).
I. P. Boglaev, “Variational-difference scheme for a boundary problem with small parameter for the highest derivative,” Zh. Vychisl. Mat. Mat. Fiz.,21, No. 4, 887–896 (1981).
I. P. Boglaev, “Numerical solution of a boundary problem with small parameter for the highest derivative on a nonuniform net,” Chislennye Metody Mekh. Sploshnoi Credy. Novosibirsk,15, No. 5, 48–58 (1984).
E. O'Riordan and M. Stynes, “A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction diffusion problem,” Math. Comput.,47, No. 176, 555–570 (1986).
O. Axelsson and G. Carey, “On the numerical solution of two-point singularly perturbed boundary-value problems,” Comput. Methods Appl. Mech. Eng.,50, 217–229 (1985).
D. G. Gordeziani, Methods of Solution of a Class of Nonlocal Boundary Problems [in Russian], Tbilisi State Univ. (1981).
V. A. Il'in and E. I. Moiseev, “Nonlocal boundary problem for the Sturm-Liouville operator and differential and difference treatments,” Dokl. Akad. Nauk SSSR,291, No. 3, 539–542 (1986).
M. P. Sapogas and R. Yu. Chegis, “Numerical solution of some nonlocal problems,” Liet. Mat. Rinkinys,27, No. 2, 348–356 (1987).
M. P. Sapogas and R. Yu. Chegis, “Problems with nonlocal condition,” Diff. Uravn.,23, No. 7, 1276–1284 (1987).
G. I. Marchuk and V. I. Agoshkov, Introduction to Projection-Net Methods [in Russian], Nauka, Moscow (1981).
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Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 28, No. 1, pp. 144–152, January–March, 1988.
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Ciegis, R. Numerical solution of a problem with small parameter for the highest derivative and a nonlocal condition. Lith Math J 28, 90–96 (1988). https://doi.org/10.1007/BF00972255
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DOI: https://doi.org/10.1007/BF00972255