Solution methods review of the stiff differential equations systems

In the study of the kinetics of the physical processes in a lead vapor laser, the unsteady self-consistent discharge kinetics model of the lead vapor laser is necessary. To develop this model, the stiff differential equations system is used. To increase the solution efficiency, a multistep method, called the Gear method, is recommended. The Gear method allows the integration step value to be varied in a wide range while providing calculation stability.