Abstract
A theoretical study of general relativistic and dynamical phenomena in the universe requires to solve Einstein's equations which are highly nonlinear and partial differential equations. For a solution of a problem with no spacetime symmetry such as merger of binary neutron stars and black holes, numerical simulation is the unique approach. "Numerical relativity" is the research field in which the methods for numerical solutions of Einstein's equations are studied. The purpose of this article is to introduce the numerical relativity. First, we describe the main procedures in numerical relativity particularly emphasizing the latest progress for the formulation of the Einstein's evolution equations. Then, the current status and the issues to be resolved are summarized. Finally, we present our latest numerical simulations for merger of binary neutron stars to a black hole and a neutron star.
