I understand some basic analysis techniques (local truncation error, global error, zero-stable, absolute stable, etc.) of numerical integration. But I find it hard to apply these techniques in practice.
In my case (a hair/cloth simulation for computer games), I usually do a numerical integration step followed by constraints resolving steps in every frame. I wonder how does constraint resolution affect the numerical integration?
Particularly, I am concerned with the following situation: in most cases the exact solution of constraints cannot be reached due to numerical error, insufficiently many iterative steps, etc.
When an error is introduced during constraint resolution, what will happen to the numerical integration in the next frame? Does this error act as external sources (inhomogeneous part) to the differential equations system?
EDIT: more background
I am using Verlet integration in my simulation. To resolve constraints I directly modify the positions. In the next temporal integration step the error in positions would contribute "ghost" velocity to the system.
My intention is to analyze the impact of this error and find a way to control the error to make my temporal integration stable and accurate to some desired order.