Picard's Iteration

[CNN]

I've just been introduced to Picard's iteration. However, despite the fact that I can apply it, I do not understand it. If
y' = f(x,y)and y(x[sub:3j1dqktv]0[/sub:3j1dqktv]) = y[sub:3j1dqktv]0[/sub:3j1dqktv]and Picard's iteration is y[sub:3j1dqktv]n[/sub:3j1dqktv](x) = y[sub:3j1dqktv]0[/sub:3j1dqktv] + intergral f(t, yn-1(t) dt
where does t come from? I haven't been able to get that part. Please any explanation will be appreciated.

Thanks

 

[royhaas]

You haven't said what the limits of integration are. The variable \(\displaystyle t\) is just a dummy variable for the integration.

 

[CNN]

Hi, I'm not worried about the limits. I know how to use the iteration. I'm just trying to understand the principles behind it, like why a dummy variable needs to be used and why the equation can't be simply integrated with respect to x , since it is a function of x. Thanks for the answer.