scholarly journals On Neutral Functional–Differential Equations with Proportional Delays

1997 ◽  
Vol 207 (1) ◽  
pp. 73-95 ◽  
Author(s):  
Arieh Iserles ◽  
Yunkang Liu
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
Proportional Delays ◽  
Functional Differential

scholarly journals Numerical solution of neutral functional-differential equations with proportional delays

2017 ◽  
Vol 7 (2) ◽  
pp. 186-194 ◽  
Author(s):  
Mehmet Giyas Sakar
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Error Function ◽  
Functional Differential Equations ◽  
Residual Error ◽  
Analysis Method ◽  
Neutral Functional Differential Equations ◽  
Proportional Delays ◽  
Homotopy Analysis ◽  
Functional Differential

In this paper, homotopy analysis method is improved with optimal determination of auxiliary parameter by use of residual error function for solving neutral functional-differential equations (NFDEs) with proportional delays. Convergence analysis and error estimate of method are given. Some numerical examples are solved and comparisons are made with the existing results. The numerical results show that the homotopy analysis method with residual error function is very effective and simple.

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