A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: ...

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

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 ...

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

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...

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 ...

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 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 ...