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EFFECTIVE APPROACHES USING COMBINATORICS TO SOLVE INVERSE PROBLEMS IN 2-D SYSTEMS

In this paper, new, effective approaches to solve third and second order difference equations are introduced. These approaches consist in the use of new computational tools constructed by the authors of this paper during previous investigations in a field of combinatorics and the Fibonacci hyperbolic trigonometry. Particularlly, to work out suitable combinatorial algorithms the monic power 1-D and 2-D polynomials generated by modyfied numerical triangles and the hyperbolic Fibonacci functions defined by succesive elements of the Fibonacci sequence are used. The construction of numerical algorithms is described and commented. The new computational approaches can be effectively applied for studies of various discrete-continuous systems which occured in practice. For example, such problems are considered like: ladder electric networks analysis, designing of 2-D digital fiters, analysis of current decey within the whole structure of the superconducting supercollider dipole magnet, solution of a heat transfer problems. Also the idea of combinatorial approach is used to solve different inverse problems particularlly identification problems. Specially, the identification of field sources in 2-D systems is studied very exatly. The elaborated algorithms are tested with special benchmark function and the also experimental verification using measurement data is done. On the basis of presented studies and results of computer simulations, it can be found that the combinatorial method of solving inverse problems is effective and easy to use. The advantages of this method are recurrence equations defind monic polynomials, a high accuracy of calculations, and ease to an implementation in the MATLAB package.