EllipticExpPrime[u, {a, b}] gives the derivative of EllipticExp[u, {a, b}] with respect to u.

Extrapolation methods are a class of arbitrary-order methods with automatic order and step-size control. The error estimate comes from computing a solution over an interval ...

CentralMoment[list, r] gives the r\[Null]^th central moment of the elements in list with respect to their mean.CentralMoment[dist, r] gives the r\[Null]^th central moment of ...

LineIntegralConvolutionPlot[{{v_x, v_y}, image}, {x, x_min, x_max}, {y, y_min, y_max}] generates a line integral convolution plot of image convolved with the vector field ...

The functions accessible with Wolfram LibraryLink make it possible to optimize numerical computations while still keeping the flexibility and generality of Mathematica. If ...

StreamPlot[{v_x, v_y}, {x, x_min, x_max}, {y, y_min, y_max}] generates a stream plot of the vector field {v_x, v_y} as a function of x and y. StreamPlot[{{v_x, v_y}, {w_x, ...

DiscretePlot3D[expr, {i, i_min, i_max}, {j, j_min, j_max}] generates a plot of the values of expr when i runs from i_min to i_max and j runs from j_min to ...

Plot3D[f, {x, x_min, x_max}, {y, y_min, y_max}] generates a three-dimensional plot of f as a function of x and y. Plot3D[{f_1, f_2, ...}, {x, x_min, x_max}, {y, y_min, ...

A method like "Newton's" method chooses a step, but the validity of that step only goes as far as the Newton quadratic model for the function really reflects the function. ...

In some cases it is useful to split the differential system into subsystems and solve each subsystem using appropriate integration methods. Recombining the individual ...