Exact Solution to Systems of Linear First-Order Integro-Differential Equations with Multipoint and Integral Conditions

2019 ◽  
pp. 1-16
Author(s):  
M. M. Baiburin ◽  
E. Providas
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Integral Conditions ◽  
First Order

scholarly journals Oscillation of Nonlinear First Order Neutral Differential Equations

2007 ◽  
Vol 4 (3) ◽  
pp. 485-490
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Integral Conditions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

scholarly journals On solving fuzzy delay differential equation using bezier curves

2020 ◽  
Vol 10 (6) ◽  
pp. 6521
Author(s):  
Ali F. Jameel ◽  
Sardar G. Amen ◽  
Azizan Saaban ◽  
Noraziah H. Man
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Delay Differential Equations ◽  
Bezier Curves ◽  
Bézier Curves ◽  
First Order ◽  
Delay Differential

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.

A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes

2004 ◽  
Vol 4 (4) ◽  
pp. 464-493 ◽  
Author(s):  
V.L. Makarov ◽  
I.P. Gavrilyuk ◽  
M.V. Kutniv ◽  
M. Hermann
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Difference Scheme ◽  
Ordinary Differential Equations ◽  
Arbitrary Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Algebraic Equations ◽  
Order Of Accuracy ◽  
First Order ◽  
Exact Difference

AbstractWe consider two-point boundary value problems for systems of first-order nonlinear ordinary differential equations. Under natural conditions we show that on an arbitrary grid there exists a unique two-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection onto the grid of the exact solution of the corresponding system of differential equations. A constructive algorithm is proposed in order to derive from the EDS a so-called truncated difference scheme of an arbitrary rank. The m-TDS represents a system of nonlinear algebraic equations with respect to the approximate values of the exact solution on the grid. Iterative methods for its numerical solution are discussed. Analytical and numerical examples are given which illustrate the theorems proved. Keywords: systems of nonlinear ordinary differential equations, difference scheme, exact difference scheme, truncated difference scheme of an arbitrary order of accuracy, fixed point iteration.

On the Oscillation of Solutions of First Order Differential Equations with Retarded Arguments

2003 ◽  
Vol 10 (1) ◽  
pp. 63-76 ◽  
Author(s):  
M. K. Grammatikopoulos ◽  
R. Koplatadze ◽  
I. P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Integral Conditions ◽  
First Order ◽  
All Solutions ◽  
Oscillation Of Solutions ◽  
First Order Differential Equations

Abstract For the differential equation where 𝑝𝑖 ∈ 𝐿 loc (𝑅+; 𝑅+), τ 𝑖 ∈ 𝐶(𝑅+; 𝑅+), τ 𝑖(𝑡) ≤ 𝑡 for 𝑡 ∈ 𝑅+, , optimal integral conditions for the oscillation of all solutions are established.

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