Solving Einstein's Equations for Binary Black Hole Spacetimes

Numerical Solution of Evolution Equations
∂ t u = Q(u, ∂ x u, x, t).
Choose a grid of spatial points, x n .
Evaluate the function u on this grid: u n (t) = u(x n , t).
u n−1
u n
u n+1
x n−1
x n
x n+1
Approximate the spatial derivatives at the grid points
∂ x u(x n ) = ∑ k D n ku k .
Evaluate Q at the grid points x n in terms of the u k : Q(u k , x n , t).
Lee Lindblom (Caltech) Binary Black Holes UW Milwaukee 10/14/2011 16 / 32