scholarly journals On the rings of formal solutions of polynomial differential equations

1998 ◽  
Vol 44 (1) ◽  
pp. 277-292 ◽  
Author(s):  
Maria-Angeles Zurro
Keyword(s):  
Differential Equations ◽  
Polynomial Differential Equations ◽  
Formal Solutions

scholarly journals Galarkin Method with GeoGebra in Differential Equations

2021 ◽  
Vol 2090 (1) ◽  
pp. 012092
Author(s):  
Jorge Olivares Funes ◽  
Pablo Martin ◽  
Elvis Valero Kari
Keyword(s):  
Differential Equations ◽  
Numerical Approximations ◽  
Formal Solutions

Abstract Let us consider d 2 y d x 2 + y = Q ( x , a ) , y ( 0 ) = y ( 1 ) = 0 , x , a ∈ ( 0 , 1 ) . . In the following paper, various differential equations will be displayed, which willbe solved using Galerkin’s numericla method and where formal solutions and their numerical approximations can be seen with GeoGebra animated Apptles.

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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