ABSTRACT
Einstein equation is a complicated system of partial differential equations and even though it can be cast as an initial value problem, obtaining solutions for physically realistic situations is a very tall order and Numerical Simulations are crucially needed. Perhaps the strongest need is felt for extracting wave forms of gravitational waves from compact sources in a variety of possible motions. The numerical simulations however have also unexpectedly revealed the critical phenomena in collapse situation and are a tool to explore issues such as cosmic censorship. In this chapter we will describe the basic ingredients of numerical relativity and highlight some of the recent developments. The primary reference is the beautiful review by Luis Lehner [96].
