NewtonCotesError[n, f, a, b] gives the error in the elementary n-point Newton-Cotes quadrature formula for the function f on an interval from a to b.

NewtonCotesWeights[n, a, b] gives a list of the n pairs {x_i, w_i} of the elementary n-point Newton-Cotes formula for quadrature on the interval a to b, where w_i is the ...

RungeKuttaOrderConditions[p, s] gives a list of the order conditions that any s-stage Runge\[Dash]Kutta method of order p must satisfy. RungeKuttaOrderConditions[p] gives the ...

Many differential equations exhibit some form of stiffness, which restricts the step size and hence effectiveness of explicit solution methods. A number of implicit methods ...

AccuracyGoal is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result.

PrecisionGoal is an option for various numerical operations which specifies how many effective digits of precision should be sought in the final result.

The equations of motion for a free rigid body whose center of mass is at the origin are given by the following Euler equations (see [MR99]). Two quadratic first integrals of ...

FindLinearRecurrence[list] finds if possible the minimal linear recurrence that generates list.FindLinearRecurrence[list, d] finds if possible the linear recurrence of ...

Mathematica allows you to perform many operations on power series. In all cases, Mathematica gives results only to as many terms as can be justified from the accuracy of your ...

Interpolation[{f_1, f_2, ...}] constructs an interpolation of the function values f_i, assumed to correspond to x values 1, 2, ... . Interpolation[{{x_1, f_1}, {x_2, f_2}, ...