Procedures for Constructing Truncated Solutions of Linear Differential Equations with Infinite and Truncated Power Series in the Role of Coefficients

2021 ◽  
Vol 47 (2) ◽  
pp. 144-152
Author(s):  
S. A. Abramov ◽  
A. A. Ryabenko ◽  
D. E. Khmelnov
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Linear Differential

scholarly journals A summability method due to linear differential equations and a uniqueness property of solutions of singular differential equations

1976 ◽  
Vol 20 (1) ◽  
pp. 41-51
Author(s):  
H. Gingold
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Formal Series ◽  
Summability Method ◽  
Linear Differential Equations ◽  
Uniqueness Property ◽  
Singular Differential Equations ◽  
Matching Process ◽  
Linear Differential ◽  
Natural Way

The purpose of this paper is to expose a method which will match a function f(z) existing in a domain D to a formal series whose radius of convergence may be zero. This matching process has to be done in a “natural way”, and has to be “regular”, which means that if a power series converges absolutely in the circle E = {z | |z|<r} then the summability function f(z) produced by our method in the domain D and matched to will coincide with in the domain E∩D. Euler, in his time, matched the function to the power series .

Application of the special series method for representing solutions of the equation of nonstationary gas flows

2007 ◽  
Vol 5 ◽  
pp. 301-306
Author(s):  
M.Yu. Filimonov
Keyword(s):  
Partial Differential Equations ◽  
Power Series ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Gas Flows ◽  
Series Method ◽  
Linear Partial Differential Equations ◽  
Special Power ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations

For the Lin-Reissner-Tsien equation describing nonstationary transonic gas flows, solutions are constructed in the form of special power series in specially chosen functions. Such a choice of functions makes it possible to find the coefficients of the series by sequential solving both ordinary linear differential equations and linear partial differential equations. The convergence of the constructed series is investigated.

scholarly journals New Method for Solving Linear Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
S. Z. Rida ◽  
A. A. M. Arafa
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Function Method ◽  
Fractional Derivatives ◽  
Linear Differential Equations ◽  
Fractional Differential ◽  
Linear Differential ◽  
Linear Fractional Differential Equations

We develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving linear differential equations of fractional order.

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