Publikacje

Abstract:

Mathematical modelling makes it possible to analyse physical phenomena which are frequently described by non-linear differential equations. Those equations can be solved by a number of numerical methods, but not all are efficient. The paper presents an approximate solution of the nonlinear problems for beam vibrations. The main aim of this work is to develop an efficient method for solving inverse nonlinear and time-dependent problems. The main idea of this method is a decomposition of a nonlinear operator into a linear and nonlinear part. Next, the Picard’s iterations are used. In each iteration a linear combination of the Trefftz functions for the linear operator is used. The nonlinearity is treated as an inhomogeneity for the linear operator. Hence, in each iteration a linear inhomogeneous equation is solved. The presented numerical examples confirm efficiency of the method in finding a stable solution of inverse nonlinear problems, even with noisy data.

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The solution of nonlinear direct and inverse problems for beam by means of the Trefftz functions