Series Solutions of Ordinary Differential Equations

2010 ◽  
pp. 19-41
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Series Solutions

scholarly journals EXPRESSIONS OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS BY STANDARD FUNCTIONS

2006 ◽  
Vol 11 (4) ◽  
pp. 399-412 ◽  
Author(s):  
Z. Navickas ◽  
L. Bikulčiene
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Series Solutions ◽  
Series Form ◽  
Finite Sum

It is well known that solutions of many ordinary differential equations allow presentation in the power series form. In the paper we introduce and analyze rigorous conditions under which the later series (solutions) can be reduced to a finite sum of standard functions. Some areas of practical applicability of the proposed algorithm are discussed.

scholarly journals Modified nonlinearities distribution Homotopy Perturbation method as a tool to find power series solutions to ordinary differential equations

Nova Scientia ◽  
2014 ◽  
Vol 6 (12) ◽  
pp. 13 ◽  
Author(s):  
Umberto Filobello-Nino ◽  
Héctor Vázquez-Leal ◽  
Yasir Khan ◽  
D. Pereyra-Díaz ◽  
A. Pérez-Sesma ◽  
...  
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Series Solutions ◽  
Homotopy Perturbation ◽  
Polynomial Coefficients ◽  
Power Series Solutions

In this article, modified non-linearities distribution homotopy perturbation method (MNDHPM) is used in order to find power series solutions to ordinary differential equations with initial conditions, both linear and nonlinear. We will see that the method is particularly relevant in some cases of equations with non-polynomial coefficients and inhomogeneous non-polynomial terms

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