I'm using a simple version of Verlet integration for a particle–particle interaction system with collisions. At the end of each iteration, I integrate like this:
verletX = ( 1.92*x[i] - 0.92*x_old[i] ) + fx[i]*0.002; verletY = ( 1.92*y[i] - 0.92*y_old[i] ) + fy[i]*0.002; x_old[i] = x[i]; y_old[i] = y[i]; x[i] = verletX; y[i] = verletY;
Can I increase its order of error (to have more precision for decreasing timesteps) using even more old data of X and Y? For now it should be less precise than a RK4, but I’m sure it’s much better than a simple Euler integration. For example can I use the data from the last eight iterations to reach RK4 levels?
The reason I’m not trying RK4 is that the calculation of forces takes too much time. However, having a copy of the old data and updating it does not. Also I don’t need exactness; I just need the system stability such that particles stay in fixed points rather than having explosive close range leaps.