Before revision: In this research work, an explicit Runge-Kutta-Fehlberg  time integration with a fourth-order compact finite difference scheme in space  is employed for solving the regime-switching pricing model.
After revision: In this research work, an explicit Runge-Kutta-Fehlberg time integration with a fourth-order compact finite difference scheme in space and a high order analytical approximation of the optimal exercise boundary is employed for solving the regime-switching pricing model.