APMonitor and Gekko solve high index Differential and Algebraic Equations (DAEs) without rearrangement or differentiation. A common method for high index DAEs is to use Pantelides algorithm to reduce the index order. The index of a DAE is the number of times the equations must be differentiated to return to index-0 (ODE) form. Most ODE and DAE solvers have several challenges:
1. Consistent initial condition is required
2. Required index-1 or index-2 (Hessenberg form)
3. Numerical drift with repeated differentiation
APMonitor and Gekko overcome these challenges by solving high index DAEs without differentiation with orthogonal collocation on finite elements and efficient sparse solvers.
See apmonitor.com/wiki/index.php/... for source code.