Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

All the functionality of NumericalMath`GaussianQuadrature`is now available in the newly created Numerical Differential Equation Analysis Package.

All the functionality of NumericalMath`NewtonCotes` is now available in the newly created Numerical Differential Equation Analysis Package.

Diagonal[m] gives the list of elements on the leading diagonal of the matrix m.Diagonal[m, k] gives the elements on the k\[Null]^th diagonal of m.

Csch[z] gives the hyperbolic cosecant of z.

Ordinary mathematical functions in Mathematica are always "listable", so that they are immediately applied in parallel across lists. Mathematica provides a wide variety of ...

ButcherBetaBar[tree] gives the number of ways of labeling tree with ButcherOrder[tree] distinct labels such that every vertex is labeled.ButcherBetaBar[n, tree] gives the ...

ButcherBeta[tree] gives the number of ways of labeling tree with ButcherOrder[tree] - 1 distinct labels such that the root is not labeled, but every other vertex is labeled. ...

ButcherColumnConditions[p, s] gives the column-simplifying conditions up to and including order p for s stages. ButcherColumnConditions[p] gives the column-simplifying ...

ButcherPhi[tree, s] gives the weight of tree in an s-stage Runge\[Dash]Kutta method. ButcherPhi[tree] gives the weight of tree in stage-independent tensor notation.