This paper describes the numerical evolution of binary black hole spacetimes using a generalized harmonic coordinate method. The method allows for the simulation of binary black hole mergers, including the plunge, merger, and ringdown phases. The study focuses on a binary system of two equal-mass, non-spinning black holes, evolving through a single plunge-orbit, merger, and ringdown. The resulting black hole is estimated to be a Kerr black hole with angular momentum parameter a ≈ 0.70. The simulation shows that the black hole mass is approximately 1.9M₀ and angular momentum J ≈ 0.70M₀². The energy radiated as gravitational waves is estimated to be about 5% of the initial rest mass of the system. The numerical method uses a discretization scheme based on harmonic coordinates, adaptive mesh refinement, dynamical excision, and constraint damping. The code is able to evolve the system for sufficient time to extract information about the merger process. The simulation results show that the black hole mass and angular momentum are consistent with the Kerr metric. The energy emitted as gravitational waves is calculated using the Newman-Penrose scalar Ψ₄, and the results suggest that about 5% of the initial mass is radiated as gravitational waves. The study highlights the importance of numerical simulations in understanding the dynamics of binary black hole mergers. The results provide insights into the behavior of gravitational waves and the properties of the final black hole. The method described is a significant step forward in the numerical simulation of binary black hole systems, and future work will focus on improving the accuracy of simulations and exploring a broader range of initial conditions.This paper describes the numerical evolution of binary black hole spacetimes using a generalized harmonic coordinate method. The method allows for the simulation of binary black hole mergers, including the plunge, merger, and ringdown phases. The study focuses on a binary system of two equal-mass, non-spinning black holes, evolving through a single plunge-orbit, merger, and ringdown. The resulting black hole is estimated to be a Kerr black hole with angular momentum parameter a ≈ 0.70. The simulation shows that the black hole mass is approximately 1.9M₀ and angular momentum J ≈ 0.70M₀². The energy radiated as gravitational waves is estimated to be about 5% of the initial rest mass of the system. The numerical method uses a discretization scheme based on harmonic coordinates, adaptive mesh refinement, dynamical excision, and constraint damping. The code is able to evolve the system for sufficient time to extract information about the merger process. The simulation results show that the black hole mass and angular momentum are consistent with the Kerr metric. The energy emitted as gravitational waves is calculated using the Newman-Penrose scalar Ψ₄, and the results suggest that about 5% of the initial mass is radiated as gravitational waves. The study highlights the importance of numerical simulations in understanding the dynamics of binary black hole mergers. The results provide insights into the behavior of gravitational waves and the properties of the final black hole. The method described is a significant step forward in the numerical simulation of binary black hole systems, and future work will focus on improving the accuracy of simulations and exploring a broader range of initial conditions.