Oscillations in Singularly Perturbed Delay Equations

1992 ◽  
pp. 164-224 ◽  
Author(s):  
A. F. Ivanov ◽  
A. N. Sharkovsky
Keyword(s):  
Delay Equations ◽  
Singularly Perturbed

scholarly journals Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
F. Z. Geng ◽  
S. P. Qian
Keyword(s):  
Boundary Layer ◽  
Present Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Approximate Solutions ◽  
Delay Equations ◽  
Singularly Perturbed ◽  
Regular Domain ◽  
Reproducing Kernel Method ◽  
Boundary Layer Problem

A numerical method is presented for solving the singularly perturbed multipantograph delay equations with a boundary layer at one end point. The original problem is reduced to boundary layer and regular domain problems. The regular domain problem is solved by combining the asymptotic expansion and the reproducing kernel method (RKM). The boundary layer problem is treated by the method of scaling and the RKM. Two numerical examples are provided to illustrate the effectiveness of the present method. The results from the numerical example show that the present method can provide very accurate analytical approximate solutions.

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