The Non-Local Existence Problem of Ordinary Differential Equations

1945 ◽  
Vol 67 (2) ◽  
pp. 277 ◽  
Author(s):  
Aurel Wintner
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Local Existence ◽  
Existence Problem ◽  
Non Local

A non-standard numerical approach to the solution of some second-order ordinary differential equations

2015 ◽  
Vol 08 (04) ◽  
pp. 1550076 ◽  
Author(s):  
A. Adesoji Obayomi ◽  
Michael Olufemi Oke
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Approach ◽  
Local Approximation ◽  
Second Order ◽  
Discrete Models ◽  
Order Ordinary Differential Equation ◽  
Non Local

In this paper, a set of non-standard discrete models were constructed for the solution of non-homogenous second-order ordinary differential equation. We applied the method of non-local approximation and renormalization of the discretization functions to some problems and the result shows that the schemes behave qualitatively like the original equation.

ON A METHOD FOR SOLVING A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 73 (1) ◽  
pp. 70-75
Author(s):  
S.M. Temesheva ◽  
◽  
P.B. Abdimanapova ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Point Boundary ◽  
Local Boundary ◽  
The Family ◽  
Non Local

In this paper, we consider a boundary value problem for a family of linear differential equations that obey a family of nonlinear two-point boundary conditions. For each fixed value of the family parameter, the boundary value problem under study is a nonlinear two-point boundary value problem for a system of ordinary differential equations. Non-local boundary value problems for systems of partial differential equations, in particular, non-local boundary value problems for systems of hyperbolic equations with mixed derivatives, can be reduced to the family of boundary value problems for ordinary differential equations. Therefore, the establishment of solvability conditions and the development of methods for solving a family of boundary value problems for differential equations are actual problems. In this paper, using the ideas of the parametrization method of D. S. Dzhumabaev, which was originally developed to establish the signs of unambiguous solvability of a linear two-point boundary value problem for a system of ordinary equations, a method for finding a numerical solution to the problem under consideration is proposed.

scholarly journals On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 220
Author(s):  
Francisco Morillas ◽  
José Valero
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Differential System ◽  
Infinite Number ◽  
Life Tables ◽  
Diffusion Modeling ◽  
Ordinary Differential System ◽  
Finite Delay ◽  
Non Local

In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.

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