Uniformly convergent methods for singularly perturbed problems

1998 ◽  
Vol 78 (S3) ◽  
pp. 1105-1106
Author(s):  
Zor. Uzelac ◽  
Kat. Surla
Keyword(s):  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
Uniformly Convergent

scholarly journals Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Habtamu Garoma Debela ◽  
Gemechis File Duressa
Keyword(s):  
Boundary Condition ◽  
Numerical Integration ◽  
Operator Method ◽  
Singularly Perturbed ◽  
Integral Boundary Condition ◽  
Singularly Perturbed Problems ◽  
Integral Boundary ◽  
Uniformly Convergent ◽  
Exponentially Fitted ◽  
Fitted Operator

In this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent.

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems
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