Flight model & calculations?

Can anybode describe me in short how it works the code and how uses the data? How is calculated the acceleration –> speed > distance for airplanes and missiles from coeffs + physical data?
What math. method and formula is used to avoid discretisation error in case using only linear albegra and interpolation method?
How accurate is the calculation?
I do not want to reprogram or copy anyting I’m just curious.

Compute all force and torque torseur by [F,Q]=1/2Rho(Z)CX,Y,Z,L,M,NSTASTAS + THRUST(Mach,alt,RPM) + Mg
Integrate non deformable solid dynamic differential equation by any kind of RungeKutta or Newton Raphson method (I do believe BMS code uses regular RK4) 
Thx.