scholarly journals Generalized quasilinearization method for nonlinear functional differential equations

2003 ◽  
Vol 16 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Bashir Ahmad ◽  
Rehmat Ali Khan ◽  
S. Sivasundaram
Keyword(s):  
Differential Equations ◽  
Rate Of Convergence ◽  
Initial Value Problems ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Monotone Sequence ◽  
Quasilinearization Method ◽  
Initial Value ◽  
Nonlinear Functional ◽  
Functional Differential

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of convergence higher than quadratic.

scholarly journals D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1761
Author(s):  
Natalia Dilna ◽  
Michal Fečkan ◽  
Mykola Solovyov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Functional Differential Equations ◽  
Linear Functions ◽  
Initial Value ◽  
Nonlinear Functional ◽  
Symmetry Properties ◽  
Theoretical Investigations ◽  
Functional Differential ◽  
Symmetric Property

This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.

scholarly journals Resolvent of nonautonomous linear delay functional differential equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Joël Blot ◽  
Mamadou I. Koné
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Differentiable Function ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Complete Proof ◽  
Right Hand ◽  
Linear Delay ◽  
Functional Differential ◽  
The Right

AbstractThe aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

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