Riccati Differential Equation with Continued Fractions

Explore the solutions of the Riccati differential equation with continued fractions, which provide a very effective function approximation toolset. Usually the continued fraction expansion of a function approximates the function better than its Taylor or Fourier series. The solution(s) of the Riccati differential equation are very diverse; they contain polynomials, trigonometric and hyperbolic functions, logarithms, and (nested) square roots.

(63 lines omitted)

The solutions of the Riccati differential equation are ratios of Bessel functions. In many cases these simplify to monomials, combinations of trigonometric functions, and logarithms. The number of terms used in the continued fraction expansion is , is the domain on the axis (" range"), and is the range of values displayed on the axis (" range").
 
Powered by Wolfram Mathematica
Give us your feedback
Give us your feedback

Source page:




 often  occasionally  never

Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed.
Privacy Policy »

Note: To run this Demonstration you need the free
Mathematica Player
or Mathematica 7+
Download or upgrade to Mathematica Player 7
I already have Mathematica Player or Mathematica 7+