The phenomenon of cavitation studies the formation, growth, and collapse of gas bubbles in a fluid, which is the product of a sudden decrease in pressure inside a liquid at a constant temperature. If the pressure decreases due to the use of ultrasonic acoustic waves, it is called acoustical cavitation; this phenomenon has many applications in different fields; there are both simple and complex mathematical models for such phenomena. In this work, we obtained the numerical solution of the Keller-Miksis equation, which is modeled using a differential equation of non-linear second order and implemented in an algorithm in MATLAB. The input of the differential equation is solved using numerical methods of adaptive step with different matched pairs, such as those of Runge-Kutta-Fehlberg and Cash-Karp. A comparative study was carried out between different simulation parameters such as execution time, number of steps, and number of functional evaluations between the adaptive step methods used. Due to the nonlinear nature of the numerical solution, especially in the oscillation zone that occurs after the first collapse, the most optimal method was Cash-Karp.