A remark on the multi-domain hybrid method for calculating the power-law decay of the gravitational radiation waveforms with analytic radiation boundary conditions (Q902960)

Summary: A hybrid method based on the multi-domain spectral and finite difference methods is considered for computing the power-law decay of gravitational radiation waveforms. For the radiation boundary condition, we adopt the analytic radiation boundary condition based on the Laplace transformation of kernel functions developed by \textit{S. R. Lau} [J. Comput. Phys. 199, No. 1, 376--422 (2004; Zbl 1127.83003)]. In this note, we present several numerical results for the orbital index \(l = 2\) with the hybrid and Lau's method. The Lau's method enables the hybrid method to obtain the power-law decay even when the computational domain is small, but the numerical results show that the proper power-law decay rate, \(p = 7\) is not obtained. Instead, we obtained \(p \sim 4\), which corresponds to the power-law decay rate extracted when the outer domain goes to \(\infty\). We remark that the system of equations or high order method with high precision is necessary for obtaining the proper decay rate.