scholarly journals On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a0(x) + a1(x) y + a2(x) y2 + … + an(x) yn

2020 ◽  
Vol 51 (1) ◽  
pp. 217-232 ◽  
Author(s):  
Antoni Ferragut ◽  
Jaume Llibre
Keyword(s):  
Differential Equations ◽  
Polynomial Differential Equations ◽  
Polynomial Solutions

Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Fractional Differential Equations ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Variable Order ◽  
Polynomial Solutions ◽  
Fractional Differential ◽  
Approximate Polynomial

AbstractIn this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

On the polynomial solutions of ordinary differential equations of the fourth order

1985 ◽  
Vol 26 (7) ◽  
pp. 1547-1552 ◽  
Author(s):  
J. S. Dehesa ◽  
E. Buendia ◽  
M. A. Sanchez‐Buendia
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Polynomial Solutions

The number of limit cycles of certain polynomial differential equations

1984 ◽  
Vol 98 (3-4) ◽  
pp. 215-239 ◽  
Author(s):  
T. R. Blows ◽  
N. G. Lloyd
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Small Amplitude ◽  
Two Dimensional ◽  
Differential Systems ◽  
Quadratic Systems ◽  
Polynomial Differential Equations ◽  
Image Position ◽  
Cubic Systems

SynopsisTwo-dimensional differential systemsare considered, where P and Q are polynomials. The question of interest is the maximum possible numberof limit cycles of such systems in terms of the degree of P and Q. An algorithm is described for determining a so-called focal basis; this can be implemented on a computer. Estimates can then be obtained for the number of small-amplitude limit cycles. The technique is applied to certain cubic systems; a class of examples with exactly five small-amplitude limit cycles is constructed. Quadratic systems are also considered.

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