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 ...

The IDA package is part of the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) developed at the Center for Applied Scientific Computing of Lawrence ...

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: ...

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 ...

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 ...

The control mechanisms set up for NDSolve enable you to define your own numerical integration algorithms and use them as specifications for the Method option of NDSolve. ...

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 ...

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 ...

A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...

Consider the matrix differential equation where the initial value y_0 y(0)∈^m×p is given. Assume that y_0^Ty_0I, that the solution has the property of preserving ...