Give to an interpolation function an analitic function with mathematica

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SUMMARY

The discussion focuses on converting an InterpolatingFunction generated by solving a differential equation using shooting methods in Mathematica into an approximate analytic form. The user seeks to express the output, represented as InterpolatingFunction[{{-0.35,0.35}},<>][theta1], in a polynomial format such as g[theta1] = a * theta1^2 + b * theta1 + c. The recommended approach to achieve this transformation is to utilize the "FindFit" function in Mathematica.

PREREQUISITES
  • Understanding of differential equations and shooting methods.
  • Familiarity with Mathematica software and its syntax.
  • Knowledge of InterpolatingFunction objects in Mathematica.
  • Basic grasp of polynomial functions and curve fitting techniques.
NEXT STEPS
  • Explore the "FindFit" function in Mathematica for curve fitting.
  • Research the properties and usage of InterpolatingFunction in Mathematica.
  • Learn about polynomial regression and its applications in data fitting.
  • Investigate advanced techniques for solving differential equations in Mathematica.
USEFUL FOR

Mathematics students, researchers in computational science, and anyone interested in numerical methods and data fitting using Mathematica.

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i have solved a differential equation with shooting methods, the output is in form of interpolate function, i can see it with a graphics, but i i would have an approssimate analitic form what kind of function i have to do ?

the equation give in output have this form..

InterpolatingFunction[{{-0.35,0.35}},<>][theta1]

where theta1 is the indipendet variable...
i would like to have a forme like :

g[theta1] = a *theta1^2+ b*theta1+ c...

how can i have this solution ?
 
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Use "FindFit"
 

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