### Math ClubNumerical differentiation: some lessons from blast calculationsJeffrey Connors (UConn)

Wednesday, April 3, 2019
5:45pm – 6:35pm

Storrs Campus
Monteith 321

Computer simulations of natural phenomena often require the calculation of derivatives for functions when the function values are only known approximately at some specific points and the standard differentiation rules from calculus are not applicable. The derivative can only be approximated using the available data. Such a technique is called numerical differentiation'', and there are infinitely many ways to do it.

In the early days of computing, scientists learned right away that different algorithms for numerical differentiation can yield very different results for simulations. In fact, it is not uncommon for methods that seem intuitive to fail completely. There is a classic test problem that comes from computing the shock wave for an explosion. We will study numerical differentiation for this problem and another related problem to learn some things about what works, what doesn't and why.

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