This work presents the simulation of a steam generator or water-tube boiler through the implementation in MATLAB® for a proposed mathematical model. Mass and energy balances for the three main components of the boiler - the drum, the riser and down-comer tubes - are presented. Three alternative solutions to the ordinary differential equation (ODE) were studied, based on Runge–Kutta 4th order method, Heun’s method, and MATLAB function Ode45. The best results were obtained using MATLAB® function Ode45 based on the Runge–Kutta 4th Order Method. The error was less than 5% for the simulation of the steam pressure in the drum, the total volume of water in the boiler, and the mixture quality in relation to what was reported.