Stability investigation of the spectral method for determining pressure distribution along the pipeline in the non-stationary case in the basis of biorthogonal polynomials
Keywords:
spectral methods, mathematical model, nonstationary gas motion, linearization, biorthogonal and quasiorthogonal polynomialsAbstract
In this paper on the basis of constructed biorthogonal polynomials authors investigated the stability
of the proposed method for solving problems of mathematical physics, in particular for
calculating unsteady gas flow in pipelines. The way of the problem solving is investigated by the
method of separation of variables in the basis of biorthogonal polynomials. The solution of the problem
is constructed as a sum of a series of biorthogonal and quasispectral polynomials. The comparative
analysis of the solution is carried out for different values of the input parameters. The
influence of the method parameters, including the order of partial sum, the functional grid, and
the error of calculations on the accuracy of obtained solution is studied. The calculation results
are presented in the form of tables.
