Numerical modeling of the eigenvalue problem for a linear ordinary differential equation with homogeneous boundary conditions using the second kind Chebyshev polynomials

One of the urgent problems of the mechanics of the continuous environment is the problem of hydrodynamic stability. This problem is reduced to solving an eigenvalue problem for an ordinary differential equation with a small parameter at the highest derivative. The article presents the results of studies of mathematical models of hydrodynamic systems of a general form, described by an eigenvalue problem for a linear ordinary differential equation under homogeneous linear boundary conditions, since studies of the stability of mathematical models of many hydrodynamic flows fall under this class of equations.

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