Numerically generated axisymmetric black hole spacetimes: Numerical methods and code tests

We develop a flexible computer code to study axisymmetric black hole spacetimes. The code is currently set up to evolve the fully nonlinear Einstein equations in azimuthal and equatorial plane symmetry. The initial data for this code generally consists of a combination of one black hole and an arbitrary amplitude, time symmetric gravitational wave. We present a discussion of the mathematical framework for the problem, various coordinate and time slice choices, and a battery of code tests.