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A numerical algorithm for the nonlinear Kirchhoff string equation

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Abstract

The initial boundary value problem is considered for the dynamic string equation . Its solution is found by means of an algorithm, the constituent parts of which are the Galerkin method, the modified Crank-Nicolson difference scheme used to perform approximation with respect to spatial and time variables, and also a Picard type iteration process for solving the system of nonlinear equations obtained by discretization. Errors of the three parts of the algorithm are estimated and, as a result, its total error estimate is obtained.

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  1. Department of Applied Mathematics and Computer Sciences, Tbilisi State University, University Street 2, Tbilisi, 0177, Georgia

    Jemal Peradze

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  1. Jemal Peradze
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Peradze, J. A numerical algorithm for the nonlinear Kirchhoff string equation. Numer. Math. 102, 311–342 (2005). https://doi.org/10.1007/s00211-005-0642-1

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  • DOI: https://doi.org/10.1007/s00211-005-0642-1

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