# Iterative methods - causality violation?

1. Apr 27, 2012

### sri sharan

Consider a partial differential equation describing the evolution of some function of a system which varies with time and space. A set of initial conditions and boundary are absolutely necessary for solving the equation. However, there are some numerical iterative methods for solving differential equations like Gauss sidel, where any arbitrary initial condition can be assumed. And yet it yields an accurate solution(with the error of approximation present obviously). So how is it that the numerical technique, which represents the differential equation was able to solve without initial conditions? How can a solution be generated with out talking the initial information which was essential for the original differential equation?

Edit: I realize that the title isn't exactly apt. However I can't change it now, so sorry about that

Last edited: Apr 27, 2012