INITIAL VALUE PROBLEM FOR A NONLINEAR SINGULAR INTEGRO-DIFFERENTIAL EQUATION

1994 ◽  
Vol 14 (3) ◽  
pp. 261-271 ◽  
Author(s):  
Linghai Zhang
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Initial Value ◽  
Integro Differential Equation

scholarly journals An existence theorem for solutions of an integro-differential equation in Banach spaces

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Differential Equation ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Initial Value Problem ◽  
Initial Value ◽  
Measures Of Noncompactness ◽  
Integro Differential Equation ◽  
Local Solutions

AbstractThe paper contains an existence theorem for local solutions of an initial value problem for a nonlinear integro-differential equation in Banach spaces. The assumptions and proofs are expressed in terms of measures of noncompactness.

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.

scholarly journals MODELLING OF URBAN TRAFFIC FLOW

2017 ◽  
Vol 1 ◽  
pp. 109 ◽  
Author(s):  
Sharif E. Guseynov ◽  
Alexander V. Berezhnoy
Keyword(s):  
Differential Equation ◽  
Mathematical Models ◽  
Traffic Flow ◽  
Initial Value Problem ◽  
Planck Equation ◽  
Continuous Model ◽  
Urban Traffic ◽  
Sufficient Condition ◽  
Initial Value ◽  
Integro Differential Equation

In this paper non-deterministic motion of urban traffic is studied under certain assumptions. Based on those assumptions discrete and continuous mathematical models are developed: continuous model is written as the Cauchy initial-value problem for the integro-differential equation, whence among other things it is obtained the Fokker-Planck equation. Besides, the sufficient condition ensuring the mathematical legitimacy of the developed continuous model is formulated.

Initial problem for a nonlinear integro-differential equation with a higher-order hyperbolic operator and with reflection of the argument

2020 ◽  
pp. 31-56
Author(s):  
T.K. Yuldashev ◽  
J.A. Artykova
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Higher Order ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Degenerate Kernel ◽  
Hyperbolic Operator ◽  
Initial Value ◽  
Partial Differential ◽  
Integro Differential Equation

In this paper it is studied the questions of one value solvability of initial value problem for nonlinear integro-differential equation with hyperbolic operator of the higher order, with degenerate kernel and reflective argument for regular values of spectral parameter. It is expressed the partial differential operator on the left-hand side of equation of higher order by the superposition of first-order partial differential operators. This is allowed us to present the considering integro-differential equation as an integral equation, describing the change of the unknown function along the characteristic. Further is applied the method of degenerate kernel. In proof of the theorem on one-value solvability of initial value problem is applied the method of successive approximations. Also is proved the stability of this solution with respect to the initial functions.

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