Акимов А. А., Абдуллина Р. И. Построение функции Римана-Грина для одного случая // Международный научный журнал "Интернаука". — 2017. — №10.

Summary. The paper deals with a problem with initial conditions for a beam equation with embedded ends. The problem was solved in two ways: as a sum of the Fourier series in the system of eigenfunctions of a one-dimensional spectral problem, and using finite-difference approximations, a numerical solution was obtained. The quantitative coincidence of the results of numerical and analytical calculations of beam deformation is obtained.

Key words: oscillations of a beam, the Euler equation, the initial-boundary conditions.

Summary: The paper deals with the history of the Riemann-Green's function. The article presents a method first used by Riemann in solving some boundary value problems for partial differential equations of hyperbolic type by comparing the two solutions, constructed in different ways.

Keywords: problem of Cauchy, Riemann-Green function, Fouier cosine transform.