Since you used

[code]

double u = _view.waveFunction.evaluate(x,t);

[/code]

to evaluate it's value in your code.

You can calculate u2=_view.waveFunction.evaluate(x,t-ddt);

And you can get du/dt with [u]u2-u/ddt[/u] if [u]ddt[/u] is small enough!

Just calculated it by definition!