Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima

In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered.  Using the method of degenerate kernel combined with the method of regularization, we obtain an implicit the first-order functional-differential equation  with the nonlinear maxima.  Initial boundary conditions are used to ensure the solution uniqueness.  In order to use the method of a successive approximations and prove the one value solvability, the obtained implicit functional-differential equ

Method of regularizing the problem of recovery of input signals of dynamic objects

The task of signal recovery is one of the most important for automated diagnostics and control systems. This task is computationally complex, especially when there are a lot of heterogeneous errors in the signals and recovery is to be performed in real time. The article deals with the application and investigation of a modified algorithm for the method of quadrature formulas for the numerical solution of the Volterra integral equations of the I kind in solving the problem of signal recovery in real time.

Three-input integral model of the recovery problem of antenna signals with interference

The problem of increasing the resolution power of an antenna through input signal recovery using the computer implementation of a mathematical model in the form of the system of three Fredholm integral equations of the first kind is examined. To solve the system of linear integral equations, regularizating algorithms and corresponding softwares based on generalized Tikhonov and Lavrentiev methods with determination of a regularization parameter by means of the model experiments technique have been developed.

Regularization method in determining of the zonal harmonic coefficients

The zonal coefficients of the gravitational field of the Earth up to degree 250 were determined from the gravity gradients measured on the satellite GOCE board. The stable solution was obtained by the Tikhonov's regularization approach. The comparison with other solutions was considered.

Regional quasigeoid solutions for the Ukraine area

The goal. The UQG2012 regional quasigeoid solution of an accuracy better than 4 cm with respect to the GPS-levelling data of the 1st and 2nd order was constructed by means of the least squares collocation method. In the first iteration the gravimetry-only quasigeoid UQG2011 was developed from the gravity anomalies for the subsequent detection of gross errors in GPS-leveling data. All terrain reductions were based on the 3x3 digital terrain model SRTM3. Scientific significance.