A class of semilinear delay differential equations with nonlocal initial conditions

2018 ◽  
Vol 15 (1) ◽  
pp. 45-60
Author(s):  
Ioan I. Vrabie
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Initial Conditions ◽  
Nonlocal Initial Conditions ◽  
Delay Differential

scholarly journals Solving delay differential equations by successive interpolations

2013 ◽  
Vol 29 (2) ◽  
pp. 133-140
Author(s):  
ALEXANDRU MIHAI BICA ◽  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Stability ◽  
Initial Conditions ◽  
Functional Differential Equations ◽  
New Method ◽  
Numerical Examples ◽  
Interpolation Procedure ◽  
Functional Differential ◽  
Delay Differential

In this paper we construct the new method of successive interpolations for functional differential equations using the interpolation procedure of cubic splines generated by initial conditions. The convergence and the numerical stability of the method are proved and tested on some numerical examples.

scholarly journals Numerical Solution of Non-linear Delay Differential Equations Using Semi Analytic Iterative Method

2019 ◽  
Vol 25 (103) ◽  
pp. 131-142
Author(s):  
Asmaa A. Aswhad ◽  
Samaher M. Yassein
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Numerical Solution ◽  
Delay Differential Equations ◽  
Initial Conditions ◽  
Linear Delay ◽  
Non Linear ◽  
Delay Differential

       We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.                       

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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