Supporting a large number of numerical integration methods for differential equations is a lot of work. In order to cut down on maintenance and duplication of code, common ...

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 ...

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 ...

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: ...

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 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 ...

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 ...

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, The derivatives of the dependent variables x are expressed explicitly in ...

The Mathematica function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations (ODEs) as well as some ...