To calculate a particle trajectory you should solve the equation of motion

dV/dt=a(x)=q_e*(E+V x B)          1)

dR/dt=V                                       2)

A simple but good algorithm is the leap frog, which solves the following equations

R(t+dt/2)=R(t-dt/2)+v(t)               3)

V(t+dt)=V(t)+a(R(t+dt/2))dt         4)

solving alternatively the velocity and position equation. 

Normal difference schemes can be unstable, introducing errors that are amplified.

For the collision part, you can choose the time of collision randomly considering that the probability of a collision after a time interval Dt is given by

P=1-exp(-VNS(v)Dt)                       5)

 Where S(v) is the total cross section and N is the density of target particles (atoms or molecules). The real equation is

dP/dt=-VNS(V)                          6)

and if V (the modulus) is constant than you have consider eq. 5.

But usually you have three types of collisions, elastic, inelastic and ionization.

Neglect ionization as first approximation, or consider it as an inelastic process so

S(V)=Se(v)+Si(v)           7)

To simplify the approach one introduce the null collision so that

V St=V*Sn(V)+V*S(V)= constant so that you again obtain eq. 5 using St.

so that St does not depend on the velocity.

Now you can proceed in two ways. 

a) With a random number r1 you can choose the collision time solving equation 5 with P=r1

b)  with r1 you decide if the collision happens in the time interval.

When a collision happens, with a second random number r2 you choose which process happens comparing r2 with Sn/ St, Se/St, Si/St. 

If the collision chosen is the null collision then nothing happens.

On the contrary, you should choose a two random numbers for the deflection angles 

r3 *2π = a1 (angle of collision plane)

r4*π = a2 (angle of deflection)

This is for isotropic collisions.

If the collision is not isotropic as elastic collisions, you should use momentum transfer cross section (so you can use as isotropic collision) or you should integrate the differential cross section. Once you have decided the collision you should consider the momentum and energy transferred in the collision to calculate the velocity after the collision. A good approximation can be to neglect the momentum transferred in elastic collisions (module of velocity is the same before and after) . But in this way you cannot measure the plasma resistance

For inelastic collision 

Epost=Ebefore-∆E that is the energy of ionization or excitation of the atoms and molecules,  If you neglect this process you could not reproduce the U-V characteristic of a Hertz lamp or any discharge.

It is not difficult do implement, but be careful of the time step the should be not too large.

Thank you, it added many thing to my knowledge.

try to use COMSOL for it as u can input equations into the software, go through plasma module help