Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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14
votes
1answer
577 views

How to guarantee that NDSolve correctly detects abrupt changes in parameters?

When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
12
votes
1answer
2k views

Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...
56
votes
9answers
3k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
42
votes
1answer
2k views

Adaptive sampling for slow to compute functions in 2D

EDIT: Although I have posted an answer based on my current progress, this in incomplete. Please see the "open issues" section in the answer. Most plotting functions in Mathematica adjust the ...
21
votes
1answer
399 views

Is there an NDSolve`ProcessEquations analog for NIntegrate?

NDSolve has an interface for repeatedly solving an equation with different initial conditions without having to analyze the equation and set up the solving algorithm each time. This can improve ...
47
votes
10answers
3k views

Can Mathematica propose an exact value based on an approximate one?

Sometimes, I use Mathematica to do some hypothesis on homeworks to make the question easier. For instance, when I have to compute big sums when $n\to\infty$ and Mathematica can't give the exact ...
21
votes
2answers
466 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...