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A numerical algorithm for the nonlinear Kirchhoff string equation

Research paper by Jemal Peradze

Indexed on: 10 Nov '05Published on: 10 Nov '05Published in: Numerische Mathematik



Abstract

The initial boundary value problem is considered for the dynamic string equation Open image in new window. 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.