scholarly journals A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

2006 ◽  
Vol 22 (1-2) ◽  
pp. 317-329
Author(s):  
T. Zheng ◽  
F. Liu
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Galerkin Method ◽  
Singularly Perturbed ◽  
Smooth Data

scholarly journals Scalar Singularly Perturbed Cauchy Problem for a Differential Equation of Fractional Order

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Burkhan Kalimbetov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cauchy Problem ◽  
Exact Solution ◽  
Small Parameter ◽  
Fractional Order ◽  
Regularization Method ◽  
Original Problem ◽  
Convergent Series ◽  
Singularly Perturbed

In this paper we consider initial problem for an ordinary differential equation of fractional order with a small parameter for the derivative. S.A. Lomov regularization method is used to construct an asymptotic approximate solution of the problem with accuracy up to any power of a small parameter. Using the computer mathematics system (CMS) Maple, a symbolic solution of the original problem is obtained, and solution schedules are constructed, depending on the initial data and various values of the small parameter. It is shown that the asymptotic solution presented in the form of a specific convergent series and the solution represented by the CMS Maple coincides with the exact solution of the original problem. 

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