### NUMERICAL INVESTIGATION OF THE INVERSE PROBLEM FOR THE BOUSSINESQ -- LOVE MATHEMATICAL MODEL

#### Abstract

The article is devoted to the numerical investigation of the inverse problem for the Boussinesq -- Love mathematical model, which describes longitudinal vibrations in a thin elastic rod taking into account inertia and external load. The inverse problem is understood as the restoration of any coefficient of the original equation, in this case, the function responsible for the external load. To find it, the method of successive approximations was used. The first paragraph presents the previously obtained results of an analytical study of this problem. The second section describes step by step an algorithm for finding an approximate solution. The third paragraph contains the results of computational experiments presented by two examples. The given examples were obtained during the implementation of the developed algorithm in the Maple software package. The results of this work can be used in further research in the field of mathematical physics or mathematical modeling.

#### Keywords

mathematical model; Boussinesq -- Love equation; inverse problem; numerical study; Sobolev type equation; method of successive approximations.

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