What Is Smart Numerics?

Smart numerics is your insurance policy against numerical errors that often lead to failures or mandate extensive redesign after you first test a physical model. You don't need to be a numerics expert to get reliable results very quickly, even with the toughest of problems.

Mathematica automatically chooses efficient algorithms.

Traditional numerics applications force users to manipulate input expressions by hand to get them into the restrictive forms that the applications require for further processing. For example, most applications require you to transform a higher-order differential equation into a system of first-order equations before entering them into the application. Mathematica's numerics automatically utilizes its symbolic capabilities to preprocess input and construct the appropriate form for its numerical algorithms. Moreover, Mathematica may repeat this strategy at any stage of the computation, choosing from and switching between a broader range of algorithms.

With Mathematica, you get unparalleled precision.

Mathematica is not limited just to machine-precision arithmetic (usually 16 digits) but can compute with a number of any size or degree of accuracy. As it is computing, it also tracks the precision of your calculations and ensures that the accuracy it ascribes to the results is justifiable.