The method of solving problems of mathematical physics, in particular for calculating a non-stationary gas flow in pipelines, is proposed in this article on the basis of the biorthogonal polynomial constructed by the authors. The method of solving the problem by means of the separation of variables in the base of biorthogonal polynomials is investigated. The analytical-approximate and approximate solutions of the problem as the sum of some biorthogonal and quasi-spectral polynomials are found. The comparative analysis between the obtained analytical-approximate and approximate solutions is conducted. The influence of parameters of methods, including the order of the partial sum, a bit grid, and an accuracy error of calculations on the obtained solution are studied. The results of calculation are presented in the form of tables.

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