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

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 ...

NDSolve is broken up into several basic steps. For advanced usage, it can sometimes be advantageous to access components to carry out each of these steps separately. NDSolve ...

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.

An integration rule computes an estimate of an integral over a region, typically using a weighted sum. In the context of NIntegrate usage, an integration rule object provides ...

An integration strategy is an algorithm that attempts to compute integral estimates that satisfy user-specified precision or accuracy goals. An integration strategy normally ...