orthogonal polynomials

The method of solving problems of mathematical physics, in particular for pressure distribution finding in the water in the underground gas storage layers on the basis of the biorthogonal polynomials constructed by the authors is proposed in the paper.  The way of the problem solving by the method of separation of variables on the basis of the biorthogonal polynomials is studied.  The solution of the problem is found in the form of the series sum of the biorthogonal and quasi-spectral polynomials.  The comparative analysis for the different values of parameters is performed.  The impact of

The mathematical model of the gas motion in the pipelines for the case where unstable process is described by the fractional time derivative is constructed in the paper. The boundary value problem is formulated. The solution of the problem is founded by the spectral method on Chebyshev-Laguerre polynomials bases with respect to the time variable and Legendre polynomials with respect to the coordinate variable. The finding of the solution eventually is reduced to the system of algebraic equations. The numerical experiment is conducted.

The investigations of the spectral methods are represented for solving applied tasks, in particular, the processing of digital information (problem of approximation, compression of information,   filtration of signals, determination of nature of physical process which is modeled), also imposition of boundary conditions for the formulated problems of mathematical physics, etc.