On global dynamics in a periodic differential equation with deviating argument

2015 ◽  
Vol 252 ◽  
pp. 446-456 ◽  
Author(s):  
Anatoli F. Ivanov ◽  
Sergei I. Trofimchuk
Keyword(s):  
Differential Equation ◽  
Global Dynamics ◽  
Deviating Argument ◽  
Periodic Differential Equation

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

Green's function for a differential equation with a deviating argument

1975 ◽  
Vol 17 (3) ◽  
pp. 259-262
Author(s):  
I. N. Inozemtseva ◽  
Yu. V. Komlenko ◽  
S. A. Pak
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Deviating Argument

scholarly journals On nonlinear boundary value problems with deviating arguments and discontinuous right hand side

1993 ◽  
Vol 6 (1) ◽  
pp. 83-91
Author(s):  
B. C. Dhage ◽  
S. Heikkilä
Keyword(s):  
Differential Equation ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
Right Hand ◽  
Nonlinear Boundary Value ◽  
The Right ◽  
Generalized Iteration

In this paper we shall study the existence of the extremal solutions of a nonlinear boundary value problem of a second order differential equation with general Dirichlet/Neumann form boundary conditions. The right hand side of the differential equation is assumed to contain a deviating argument, and it is allowed to possess discontinuities in all the variables. The proof is based on a generalized iteration method.

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