scholarly journals NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM INCLUDING BOTH DELAY AND BOUNDARY LAYER

2018 ◽  
Vol 23 (4) ◽  
pp. 568-581 ◽  
Author(s):  
Erkan Cimen
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Boundary Value Problem ◽  
Delay Differential Equation ◽  
Order Parameter ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
First Order ◽  
Delay Differential

Difference method on a piecewise uniform mesh of Shishkin type, for a singularly perturbed boundary-value problem for a nonlinear second order delay differential equation is analyzed. Also, the method is proved that it gives essentially first order parameter-uniform convergence in the discrete maximum norm. Furthermore, numerical results are presented in support of the theory.

BOUNDARY VALUE PROBLEM WITH SHIFT FOR A FRACTIONAL ORDER DELAY DIFFERENTIAL EQUATION

2019 ◽  
pp. 16-25
Author(s):  
М.Г. Мажгихова
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Delay Differential Equation ◽  
Solvability Condition ◽  
Boundary Value ◽  
Explicit Representation ◽  
Existence And Uniqueness Theorem ◽  
The Green Function ◽  
Delay Differential

В работе доказана теорема существования и единственности решения краевой задачи со смещением для дифференциального уравнения дробного порядка с запаздывающим аргументом. Решение задачи выписано в терминах функции Грина. Получено условие однозначной разрешимости и показано, что оно может нарушаться только конечное число раз. In this paper we prove existence and uniqueness theorem to a boundary value problem with shift for a fractional order ordinary delay differential equation. The solution of the problem is written out in terms of the Green function. We find an explicit representation for solvability condition and show that it may only be violated a finite number of times

scholarly journals Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation

2019 ◽  
Vol 4 (6) ◽  
pp. 1471-1482
Author(s):  
Mandeep Kaur Vaid ◽  
Geeta Arora
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Numerical Treatment ◽  
Spline Collocation ◽  
Third Order ◽  
B Spline ◽  
Collocation Technique ◽  
Delay Differential

In this paper, a class of third order singularly perturbed delay differential equation with large delay is considered for numerical treatment. The considered equation has discontinuous convection-diffusion coefficient and source term. A quintic trigonometric B-spline collocation technique is used for numerical simulation of the considered singularly perturbed delay differential equation by dividing the domain into the uniform mesh. Further, uniform convergence of the solution is discussed by using the concept of Hall error estimation and the method is found to be of first-order convergent. The existence of the solution is also established. Computation work is carried out to validate the theoretical results.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

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