The bondi problem revisited: A spectral domain decomposition code

In this paper, we present a simple domain decomposition code based on the Galerkin-Collocation method to integrate field equations of Bondi problem. The algorithm is stable, exhibits exponential convergence when considering formula as an error measure, and computationally economical. We have incorporated features both Galerkin Collocation methods along with establishment two nonoverlapping subdomains. further applied show decay mass in nonlinear regime its power-law late-time decay. Another application determination waveforms at future null infinity connected distinct initial data.