Mathematical model of an ideal capacitor

[krayvonk]

Im looking on the net for one so I can code a circuit simulator,   anyone can help with a link or short tutorial?

[ahbushnell]

The voltage on the capacitor is the integral of the current divided by the capacitance from 0 to the present time plus add the initial voltage on the capacitor.

https://en.wikipedia.org/wiki/Capacitor#Overview

Or find a basic book on circuit theory. 

While your at it you can model an inductor.

The current is the integral of the voltage across the inductor from 0 to the present time.

[IanB]

Im looking on the net for one so I can code a circuit simulator,   anyone can help with a link or short tutorial?

This is very elementary, so I am unsure how you can code a circuit simulator without any apparent knowledge of electronic circuits or physics?

But leaving that unfortunate complaint aside, an ideal capacitor has the following model. Bear in mind that no real capacitor obeys this model, and using such a model may lead to odd results.
$$i=C {\mathrm{d}v \over \mathrm{d}t}$$