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Difference schemes for fourth-order one-dimensional equations with nonlinear boundary condition

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Abstract

A difference scheme is constructed for a boundary-value problem for a one-dimensional biharmonic equation with nonlinear boundary condition. Under the hypothesis that the exact solution of the problem belongs to the Sobolev space W 2 k(Ω),k ∃[2, 4], in the lattice norm L 2 (Ω), an estimate is obtained of the precision of the difference scheme to O(hk−1,5).

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Literature cited

  1. I. P. Gavrilyuk, R. D. Lazarov, V. L. Makarov, and S. P. Pirnazarov, “Estimates of the rate of convergence of difference schemes for fourth-order elliptic equations with solutions of class W2 3 and W2 4,” Zh. Vychisl. Mat. Mat. Fiz.,23, No. 2, 355–365 (1983).

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Authors and Affiliations

  1. Kiev State University, Kiev

    I. P. Gavrilyuk & L. D. Grekov

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  1. I. P. Gavrilyuk
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  2. L. D. Grekov
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Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 43–50, 1989.

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Gavrilyuk, I.P., Grekov, L.D. Difference schemes for fourth-order one-dimensional equations with nonlinear boundary condition. J Math Sci 67, 3064–3069 (1993). https://doi.org/10.1007/BF01098141

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  • DOI: https://doi.org/10.1007/BF01098141

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