scholarly journals An Exponentially Fitted Method for Singularly Perturbed Delay Differential Equations

2009 ◽  
Vol 2009 (1) ◽  
pp. 781579 ◽  
Author(s):  
Fevzi Erdogan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Singularly Perturbed ◽  
Exponentially Fitted ◽  
Exponentially Fitted Method ◽  
Delay Differential

scholarly journals A Numerical Technique for Solving Nonlinear Singularly Perturbed Delay Differential Equations

2018 ◽  
Vol 23 (1) ◽  
pp. 64-78 ◽  
Author(s):  
A.S.V. Ravi Kanth ◽  
P. Murali Mohan Kumar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Technique ◽  
Singularly Perturbed ◽  
Spline Method ◽  
Numerical Examples ◽  
Exponentially Fitted ◽  
Delay Differential ◽  
Quasilinearization Technique

This paper presents a numerical technique for solving nonlinear singu- larly perturbed delay differential equations. Quasilinearization technique is applied to convert the nonlinear singularly perturbed delay differential equation into a se- quence of linear singularly perturbed delay differential equations. An exponentially fitted spline method is presented for solving sequence of linear singularly perturbed delay differential equations. Error estimates of the method is discussed. Numerical examples are solved to show the applicability and efficiency of the proposed scheme.

scholarly journals An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Süleyman Cengizci
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
Delay Differential Equations ◽  
Numerical Procedure ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Singularly Perturbed ◽  
Convection Term ◽  
Linear Delay ◽  
Delay Differential

In this work, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show efficiency of this numerical-asymptotic hybrid method, we compare the results with exact solutions if possible; if not we compare with the results that are obtained by other reported methods.

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