On an estimate of solutions of a linear homogeneous Volterra integro-differential equation of the first order in the critical case on the half-line

2016 ◽  
Vol 52 (8) ◽  
pp. 1030-1035
Author(s):  
S. Iskandarov
Keyword(s):  
Differential Equation ◽  
Critical Case ◽  
Half Line ◽  
Integro Differential Equation ◽  
First Order

scholarly journals APPROXIMATE SOLUTION OF A NONLINEAR INTEGRO-DIFFERENTIAL EQUATION BY THE NEWTON-KANTOROVICH METHOD

2020 ◽  
pp. 609-614
Author(s):  
I.A. Usenov ◽  
Yu.V. Kostyreva ◽  
S. Almambet kyzy
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Approximate Solution ◽  
Initial Value Problem ◽  
Nonlinear Integral Equation ◽  
Initial Problem ◽  
Initial Value ◽  
Kantorovich Method ◽  
Integro Differential Equation ◽  
First Order

In this paper, we propose a method for studying the initial value problem for a first-order nonlinear integro-differential equation. The initial problem is reduced by substitution to a nonlinear integral equation with the Urson operator. To construct a solution to a nonlinear integral equation, the Newton-Kantorovich method is used.

Central forces and secular perihelion motion

2007 ◽  
Vol 85 (10) ◽  
pp. 1045-1054 ◽  
Author(s):  
M M D'Eliseo
Keyword(s):  
Differential Equation ◽  
General Formula ◽  
Elliptical Orbit ◽  
New Method ◽  
Secular Motion ◽  
Integro Differential Equation ◽  
First Order ◽  
Light Rays ◽  
Radial Forces ◽  
Central Forces

The first-order orbital equation and its perturbed version under the form of an integro-differential equation provide a new method to study, respectively, the elliptical orbit and the secular motion of a planetary perihelion due to the perturbing action of an important category of central forces: the inverse-power radial forces. For this, a general formula is found. The related problems of the gravitational bending of fast particles and light rays are studied using the same methods. PACS Nos.: 02.60.Nm, 04.25.–g, 46.15.Ff, 45.50.Pk

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