Analytic solutions of differential-functional equations

1990 ◽  
Vol 42 (8) ◽  
pp. 952-959 ◽  
Author(s):  
A. N. Murovtsev
Keyword(s):  
Functional Equations ◽  
Analytic Solutions

Analytic Solutions of Functional Equations

10.1142/6755 ◽  
2008 ◽  
Author(s):  
Sui Sun Cheng ◽  
Wenrong Li
Keyword(s):  
Functional Equations ◽  
Analytic Solutions

Analytic solutions of systems of functional equations

1991 ◽  
Vol 43 (2) ◽  
pp. 127-129
Author(s):  
S. Z. Kurbanshoev
Keyword(s):  
Functional Equations ◽  
Analytic Solutions

Analytic Solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker Equations

1998 ◽  
Vol 08 (02) ◽  
pp. 347-357 ◽  
Author(s):  
K. M. Briggs ◽  
T. W. Dixon ◽  
G. Szekeres
Keyword(s):  
Real Line ◽  
Singular Solution ◽  
Functional Equations ◽  
Numerical Approximation ◽  
Analytic Solutions ◽  
Substantial Improvement ◽  
Circle Maps ◽  
Universal Scaling ◽  
Iterated Maps ◽  
Alternative Description

The Cvitanović–Feigenbaum (CF) equation arising in the universal scaling theory of iterated maps of the real line has strong links with the classical Schröder and Abel functional equations. This link is exploited to obtain information about the analytic solutions, and specifically the singular solution, of the CF equation, providing an alternative description of the latter to that of Eckmann and Wittwer. We obtain an accurate numerical approximation to this singular solution, using special techniques to handle the divergent series. This accuracy is a substantial improvement on previous estimates of the solution, and of the associated asymptotic feigenvalues α and δ. The solutions of the Feigenbaum–Kadanoff–Shenker equation for universal scaling in circle maps are shown to yield to the same analysis, producing accurate numerical values for the associated α and δ.

Analytic Solutions of Some Functional Equations

1972 ◽  
Vol s2-4 (3) ◽  
pp. 418-424 ◽  
Author(s):  
M. Kuczma ◽  
W. Smajdor
Keyword(s):  
Functional Equations ◽  
Analytic Solutions

scholarly journals Analytic solutions of iterative functional equations

2002 ◽  
Vol 270 (1) ◽  
pp. 200-209 ◽  
Author(s):  
Xinhe Liu ◽  
Jiehua Mai
Keyword(s):  
Functional Equations ◽  
Analytic Solutions
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