New variables recently introduced by Abhay Ashtekar will be used to calculate numerically solutions to Einstein's equations corresponding to plane gravitational waves propagating on spacetimes of finite spatial extent. The results of the computations will be compared with known exact analytical solutions, approximate analytical solutions, and numerical solutions obtained by other authors using conventional variables. It is expected that this new computer code will result in more rapid computation with greater accuracy. Generalizations of the technique, including the incorporation of matter sources, the relaxation of symmetry requirements, and changes of spatial topologies, will lead to potent new tools for studying problems of current astrophysical interest. In particular, a new approach will be available to study the relation between non-linear gravitational wave interaction and the formation of galaxies, and to generate numerically the radiative spacetimes of two interacting black holes.
