Ordinary Differential Equation (ODE)

Synonyms

ODE

Definition

An ordinary differential equation is an equality that involves a function and its derivatives with respect to only one independent variable.

Ordinary differential equations (ODEs) are frequently used for modeling biological systems to characterize the dependence of certain properties on time (Klipp et al. 2005). This time behavior can be described by a set of ODEs:

$$ \frac{{d{x_i}}}{{dt}} \;= {f_i} \ \left( {{x_1}, \ldots, {x_n},{p_1}, \ldots, {p_l},t} \right)\quad i = 1, \ldots, n $$

(1)

where x _i represents the model variables, p _j represents the parameters, and t is the time.

More generally, an implicit ordinary differential equation of order n has the form

$$ F\left( {t,x,x', \ldots, {x^{(n)}}} \right) = 0 $$

(2)

and includes the independent variable t, the unknown function x, and its derivatives up to the n-th order.

Cross-References

Optimal Experiment Design