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Search Results: 1 - 10 of 5804 matches for " Igor Petrovich Dobrovolsky "
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The Integral Equation, Corresponding to the Ordinary Differential Equation  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2014, DOI: 10.4236/oalib.1101058
Abstract: The differential operator of the ordinary differential equation (ODE) is represented as the sum of two operators: basic and supplementing operators. The order of the higher derivatives of a basic operator and ODE operator should coincide. If the basic operator has explicit system of fundamental solutions it is possible to make integral equation Volterra of II kind. For linear equations the approximate solutions of the integral equation are system of the approximate fundamental solutions of the initial ODE.
Hydrodynamical Phenomena at Preparation of Earthquake  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2014, DOI: 10.4236/oalib.1100896
Abstract: Variations in level of fluid in wells caused by Earth tides and earthquakes are governed by two leading processes: deformation of medium and filtration. These processes are described by identical systems of equations and are united by the term “hydrodynamical phenomena”. The exact solution is obtained for the problem of level variations in wells due to Earth tides. The similar problem is solved for short-term precursors of a tectonic earthquake. Results are consistent with data of field observations.
Unidimensional Inhomogeneous Isotropic Elastic Half-Space  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2015, DOI: 10.4236/oalib.1101670
Abstract: The homogeneous system of the equations of the linear theory of elasticity for the isotropic environment with one-dimensional continuous heterogeneity is considered. Bidimensional transformation Fourier is applied and the problem for images is led to the ordinary differential equations. Generally, the differential equations are transformed in integro-differential and the algorithm of such transformation is resulted. Solutions of specific problems are resulted.
The Estimation of the Error at Richardson’s Extrapolation and the Numerical Solution of Integral Equations of the Second Kind  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2015, DOI: 10.4236/oalib.1102051
Abstract: The mode of definition of the error at polynomial Richardson’s extrapolation is described. Along with the table of extrapolations the new magnitudes reflecting expediency and efficiency of extrapolation are entered. On concrete examples it is shown that application of Richardson’s extrapolation to a solution of integral equations has appeared rather effective and gives a solution with a high exactitude. Application of formulas of interpolation leads to a solution in the analytical aspect.
About the Integral Equations for Calculation of Green’s Tensor in Elastic Inhomogeneous Medium  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2016, DOI: 10.4236/oalib.1103077
Abstract:
The scheme of creation of systems of the integro-differential equations for evaluation of Green’s function in non-uniform elastic boundless medium is described. The summand with singularity is allocated. The isotropic medium with constant coefficient of Poisson and unidimensional inhomogeneous isotropic medium are considered.
The Precursor of Tectonic Earthquake in Telluric Current  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2017, DOI: 10.4236/oalib.1103488
Abstract:
The calculation of the precursor of the tectonic earthquake in the telluric current is carried out on the basis of the main equations of the telluric current and the theory of preparation of the tectonic earthquake. Results do not contradict data of field observations. Methodical significance of work is especially important.
Quasi-Quadrature Solution of Integral Equations Fredholm of the Second Kind in the Class of Integrable Functions  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2019, DOI: 10.4236/oalib.1105736
Abstract:
The analog of the quadrature solution of the equation of Fredholm of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Computing examples show expediency of such approach in appropriate cases.
Quasiquadrature Solution of the Linear Integral Equations of the Second Kind in the Class of Integrable Functions  [PDF]
Igor Petrovich Dobrovolsky
Open Access Library Journal (OALib Journal) , 2020, DOI: 10.4236/oalib.1106069
Abstract:
The analog of the quadrature solution of the equation of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Equations of Fredholm and Volterra are considered. The graphical representation of the solution is discussed. Computing examples show expediency of such approach in appropriate cases.
One Dimensional Relativistic Particle in a Quadratic Dissipative Medium Subjected to a Force That Depends on the Position  [PDF]
Federico Petrovich
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.69122
Abstract: We will find a constant of motion with energy units for a relativistic particle moving in a quadratic dissipative medium subjected to a force which depends on the position. Then, we will find the Lagrangian and the Hamiltonian of the equation of motion in a time interval such that the velocity does not change its sign. Finally, we will see that the Lagrangian and Hamiltonian have some problems.
A New Formulation of Classical Mechanics—Part 1  [PDF]
Federico Petrovich
Journal of Applied Mathematics and Physics (JAMP) , 2016, DOI: 10.4236/jamp.2016.42048
Abstract: This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the principle of least action. In this paper, we will find a third formulation that is totally different and has some advantages in comparison with the other two formulations.
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