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 ...

The method "DoubleStep" performs a single application of Richardson's extrapolation for any one-step integration method. Although it is not always optimal, it is a general ...

InverseContinuousWaveletTransform[cwd] gives the inverse continuous wavelet transform of a ContinuousWaveletData object cwd. InverseContinuousWaveletTransform[cwd, wave] ...

It is often useful to carry out a numerical integration using fixed step sizes. For example, certain methods such as "DoubleStep" and "Extrapolation" carry out a sequence of ...

This loads packages containing some test problems and utility functions. One of the first and simplest methods for solving initial value problems was proposed by Euler: ...

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

Implicit Runge–Kutta methods have a number of desirable properties. The Gauss–Legendre methods, for example, are self-adjoint, meaning that they provide the same solution ...

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 ...

It is often useful to be able to detect and precisely locate a change in a differential system. For example, with the detection of a singularity or state change, the ...