Numerical calculus using iteration for solving differential equation

Dear people,

How to make simple iteration in Mathematica for this three equations and save q for each step. If we define q'=dq/dx, q''=dq'/dx we have two equations

(1) q''[j+1]=a1*(q[j+1]-q[j])-a3*q'[j]-a5*q''[j],

(2) q'[j+1]=a2*(q[j+1]-q[j])+a4*q'[j]+a6*q''[j],

And we should substitute in third

(3) q[j+1]=Q2*q[j]+Q3*q'[j]+Q4*q''[j]

ai and Qk (i=1,..,6; k=1,2,3) are functions of delta{x}. Where delta{x}=0.01 for example. For each delta{x} I need q.

Regards,