Literature Cited
V. A. Ambartsumyan, “On the problem of diffusive reflection of light by an opaque medium,” Dokl. Akad. Nauk SSSR,38, No. 8, 257–262 (1943).
R. Bellman and E. Angel, Dynamic Programming and Partial Differential Equations, Academic Press, New York (1972).
G. V. Isakhanov, V. K. Chibiryakov, and A. M. Smolyar, “Numerical-analytic method of solution of problems of statics of thick nonhomogeneous membranes,” in: Proceedings of the 13th All-Union Conference on the Theory of Membranes and Shells [in Russian], Tallin (1983), Vol. 2, pp. 130–135.
J. Casti and R. Kalaba, Imbedding Methods in Applied Mathematics, Addison-Wesley, Reading Massachusetts (1973).
T. Y. Na, Computational Methods in Engineering Boundary-Value Problems, Academic Press, New York (1979).
S. K. Nikitin, “Application of the invariant imbedding method to the solution of planar problems of the theory of elasticity,” Sopr. Mater. Teor. Sooruzh., No. 33, 103–108 (1978).
S. K. Nikitin, “Application of the method of invariant imbedding to the determination of low frequencies of free oscillations of membranes,” in: Numerical Methods for the Solution of Problems of Construction Mechanics [in Russian], Izd. Kiev Inzh.-Stroit. Inst., Kiev (1978), pp. 107–112.
S. K. Nikitin, “Application of the method of invariant imbedding for the solution of axisymmetric problems of the theory of elasticity,” Dokl. Akad. Nauk SSSR, Ser. A, No. 8, 640–643 (1979).
S. K. Nikitin, “Numerical study of wave processes in a duct of arbitrary cross section,” Prikl. Mekh.,18, No. 6, 86–91 (1982).
S. K. Nikitin, “Influence of the intensity of a pulsed action on the fluid splashing in a container,” Kosm. Issled. Ukr., No. 16, 88–93 (1982).
S. K. Nikitin, “Analysis of transition processes of interaction of elastic bodies of revolution with a fluid”, Prikl. Mekh.,19, No. 3, 60–65 (1983).
S. K. Nikitin, “Dynamics of an elastic cylinder with fluid under a short load”, Prikl. Mekh.,20, No. 8, 83–88 (1984).
A. G. Razdol'skii, “On the realization of the invariant imbedding scheme on the basis of the relationships of the method of initial parameters,” Stroit. Mekh. Raschet Sooruzh., No. 2, 44–47 (1980).
N. P. Fleishman and I. A. Zonenashvili, “Application of the imbedding method to the calculation of membranes with edges of variable rigidity,” Soobshch. Akad. Nauk Gruz SSR,108, No. 2, 17–21 (1982).
N. P. Fleishman, R. N. Shvets, and R. I. Kalita, “Application of the invariant imbedding method to the numerical solution of two-point boundary-value problems of the theory of shells,” Mat. Metody Fiz.-Tekh. Polya, No. 16, 56–60 (1982).
G. Hall and J. M. Watt, Modern Numerical Methods for Ordinary Differential Equations, Oxford Univ. Press (1976).
V. K. Khomutskii and V. K. Chibiryakov, “On the application of the invariant imbedding method to the calculation of one-dimensional systems by the method of displacements,” Izv. Vyssh. Uchebn. Zaved., Stroit. Arkhit., No. 1, 44–47 (1983).
V. K. Chibiryakov, “On the application of the invariant imbedding method to the solution of boundary-value problems of construction mechanics,” Sopr. Mater. Teor. Sooruzh., No. 36, 77–81 (1980).
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Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Kiev Civil Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 23, No. 2, pp. 17–23, February, 1987.
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Nikitin, S.K., Chibiryakov, V.K. Solution of some problems of continuum mechanics by the method of invariant imbedding. Soviet Applied Mechanics 23, 120–126 (1987). https://doi.org/10.1007/BF00889006
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DOI: https://doi.org/10.1007/BF00889006