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 ...

When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

The basic idea behind the "StiffnessSwitching" method is to provide an automatic means of switching between a nonstiff and a stiff solver. The "StiffnessTest" and ...

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 ...

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...

Ways to construct nested lists. This generates a table corresponding to a 2×3 nested list. This generates an array corresponding to the same nested list.

Explicit representations of newlines and tabs in strings. This prints on two lines. In InputForm there is an explicit ∖n to represent the newline.

The Mathematica function NIntegrate is a general numerical integrator. It can handle a wide range of one-dimensional and multidimensional integrals. Finding a numerical ...

While most built-in Mathematica functions follow the standard evaluation procedure, some important ones do not. For example, most of the Mathematica functions associated with ...

This dialog displays information regarding the editing times of the input notebook. This is a "live" dialog that dynamically updates as changes are made to the notebook. It ...