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Positive difference operators of any preassigned order of approximation for the second derivative

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Ukrainian Mathematical Journal Aims and scope

Abstract

Difference operators are stuied, constructed by the method of block approximation for the differential operator −d 2/dt 2 with homogeneous first boundary conditions. For separators of any order of approximation the positivity property is established.

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References

  1. M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pustyl'nik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow (1966).

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  2. N. N. Gudovich, “On a new method for constructing stable difference schemes of any preassigned order of approximation for ordinary differential equations,” Zh. Vychisl. Mat. Mat. Fiz.,15, No. 4, 931–945 (1975).

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Authors and Affiliations

  1. Scientific-Research Institute of Mathematics, Voronezh University, USSR

    A. A. Terteryan

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  1. A. A. Terteryan
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1590–1597, November, 1992.

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Terteryan, A.A. Positive difference operators of any preassigned order of approximation for the second derivative. Ukr Math J 44, 1465–1472 (1992). https://doi.org/10.1007/BF01071522

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  • DOI: https://doi.org/10.1007/BF01071522

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