A numerical algorithm for the nonlinear Kirchhoff string equation

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.