Here is a list of useful references relating to ODE, Gazebo, simulation research, and other simulators.
ODE
Currently, ODE has a more accurate but slower LCP solver step.cpp using Dantzig's algorithm and a iterative quickstep.cpp algorithm which solves LCP by successive-over-relaxation (SOR) of Projected Gauss-Seidel (PGS) algorithm. Worth noting here is how ODE removes drif of joint position constraints by imposing a custom Error Reduction Parameter (ERP) and improves overall numerical stability via special Constraint Force Mixing (CFM) matrix as described in ODE's users manual.
Some notes on ODE algorithm.