Throughout many fields of science and engineering, the need for describing waveequations is crucial. Solving the wave equation for high-frequency waves istime-consuming, requires a fine mesh size and memory usage. The main goal wasimplementing and comparing different solution methods for high-frequency waves.Four different methods have been implemented and compared in terms of runtimeand discretization error. From my results, the method which performs the best is thefast sweeping method. For the fast marching method, the time-complexity of thenumerical solver was higher than expected which indicates an error in myimplementation.