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Convergence rate of Kantorovich's method for nonlinear differential equations

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Literature cited

  1. M. M. Vainberg, Variational Methods for Investigating Nonlinear Operators [in Russian], Gostekhizdat, Moscow (1956).

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  2. M. M. Vainberg, The Variational Method and Method of Monotonic Operators in Theory of Nonlinear Equations [in Russian], Nauka, Moscow (1972).

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  3. W. V. Petryshyn, “On the extension and the solution of nonlinear operator equations,” Illinois J. Math.,10 No. 2, 255–274 (1966).

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  4. L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Fizmatgiz, Moscow-Leningrad (1962).

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  5. R. S. Varga, Functional Analysis and Theory of Approximation in Hilbert Space [Russian translation], Mir, Moscow (1974).

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  6. A. Yu. Luchka and M. V. Zhuk, “The convergence rate of Kantorovich' s method for linear elliptic differential equations,” in: Methods of Qualitative and Quantitative Investigation of Differential and Integral Equations [in Russian], Izd. Instituta Matematiki Akad. Nauk UkrSSR (1975).

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, USSR

    M. V. Zhuk

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  1. M. V. Zhuk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 28, No. 2, pp. 183–193, March–April, 1976.

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Zhuk, M.V. Convergence rate of Kantorovich's method for nonlinear differential equations. Ukr Math J 28, 139–146 (1976). https://doi.org/10.1007/BF01085903

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  • DOI: https://doi.org/10.1007/BF01085903

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