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Interpolating Objects
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Solutions to complex differential equations are easy to plot accurately because interpolating functions are used to represent them.

Mathematica is unique in returning the results of numerical superfunctions (e.g. NDSolve) as symbolic functions representing the interpolation through ordinates taken--the interpolating object. This is in contrast to purely numerical systems, which return an unprocessed list of numbers.

Interpolating objects make results easily and immediately usable: for example, plotting, differentiating, or finding a specific value (whether or not it was picked for evaluation during the computation) can all be performed with a result as if it were any built-in mathematical function.

Related Links
Function documentation: InterpolatingFunction, NDSolve
The Mathematica Book: Sections Numerical Differential Equations, Approximate Functions and Interpolation



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