In the MPS method, the Navier-Stokes equations are divided into two stages, and all terms are solved explicitly, except for the pressure term, which is solved implicitly.
1. Explicit calculations of terms except the pressure term
2. Implicit calculation of pressure
3. Velocity and position correction by the pressure gradient
Where 
is the particle number density, and
is the particle number
density at the initial state.
Superscript 
expresses the time step.
Superscript * expresses a physical quantity at the stage where the explicit calculation has been completed.