**Ordinary differential equations**, or ODE's, used in numerical analysis, express a function via its derivative, and are often used to model physical systems mathematically.

## See Also

- Bernoulli

- Differentiation and steepest-descent

- DsTool
- A Tk program for exploring dynamical systems.

- minsky
- A program for simulating of models (particularly from economics) defined in terms of couple ordinary differential equations.

- Runge-Kutta
- A numeric method for solving ODE's.

- Runge-Kutta-Fehlberg
- Another numeric method, derived from Runge-Kutta, for solving ODE's.

- math
- AM A number of the commonly used numerical methods can be found in Tcllib's math module.

- tclode
- A Tcl extension that uses ODEPACK to solve differential equations.

## Description

Radioactive decay, for example, proposes that the rate of decay is purely dependent on the number of atoms that have not yet decayed, so Rate of Change of Number = -constant*number.

or d/dt(Number) = -constant*number

The solution to this trivial (can such an important equation be trivial?) equation is

N=N0 * exp (-constant * time).

where N0 is the number of atoms at time = 0. (Just differentiate the function).

If constant is negative then the number of atoms would grow. This situation can occur for living organisms - the number of new babies is proportional to the number of adults.

Partial Differential Equations are much tougher to solve, particularly in 3 dimensions. Many solver programs exist, but few are suitable for Tcl (a fully compiled language is indicated).

## Page Authors

- anonymous
- Original author.

- am
- Added some notes.

- pyk
- Various changes.