A method for approximate restoration of two coefficients in a problem for an equation of oscillations with a nonclassical boundary condition
Alexey Yurievich Shcheglov1,2, Oksana Alekseevna Andeyanova2
1MSU-SPI University in Shenzhen, Shenzhen, China
2Lomonosov Moscow State University, Moscow, Russia
Keywords: oscillation equation, nonclassical boundary condition, restoration of coefficients, iterative algorithm
Abstract
A method is proposed for restoring two coefficients in a mixed boundary value problem for an inhomogeneous hyperbolic partial differential equation of the second order based on additional information about the solution of the boundary value problem for a given fixed value of the spatial argument of the solution. The problem simulates the propagation of small transverse vibrations of a finite string with an end affected by the gravity of a body with varying mass. The proposed algorithm provides a sequential restoration of the multiplier in the heterogeneity of the oscillation equation and the coefficient in the nonclassical boundary condition based on the values of one additional function of one argument.
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