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



** See Also **

   [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%|%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.

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