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Difference schemes for solving the Cauchy problem for a second-order operator differential equation

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Abstract

A class of finite-difference schemes for solving an ill-posed Cauchy problem for a second-order linear differential equation with a sectorial operator in a Banach space is studied. Time-uniform estimates of the convergence rate and the error of such schemes are obtained. Previously known estimates are improved due to an optimal choice of initial data for a difference scheme.

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Authors and Affiliations

  1. Mari State University, pl. Lenina 1, Yoshkar-Ola, 424000, Russia

    M. M. Kokurin

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  1. M. M. Kokurin
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Correspondence to M. M. Kokurin.

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Original Russian Text © M.M. Kokurin, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 4, pp. 569–584.

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Kokurin, M.M. Difference schemes for solving the Cauchy problem for a second-order operator differential equation. Comput. Math. and Math. Phys. 54, 582–597 (2014). https://doi.org/10.1134/S0965542514040083

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  • DOI: https://doi.org/10.1134/S0965542514040083

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