ODE

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A system of ordinary differential equations (an ODE system) can be defined

\bold{y}' = \bold{f} \left(t,\bold{y} \right)

where \bold{y} is a vector of variables and \bold{y}' is the corresponding vector of derivatives with respect to the 'time' or 'independent' variable t. Written in the above form, we can always be sure that we can calculate the derivatives of the state variables providing the current state is known.

LSODE is an ODE solver for ASCEND that allows algebraic equations to be solved first, then the derivatives integrated.