Date of Award


Degree Type


Degree Name

Master of Science


Applied Mathematics


Dr. Greg J. Reid


Complicated nonlinear systems of ordinary differential equation with constraints (so- called differential algebraic equation (DAE)) arise frequently in applications, and are often so complicated that they are in practice automatically generated by computer modeling and simulation environments. We used the MapleSim software to generate such systems. Missing constraints arising by prolongation (differentiation) of the DAE need to be determined to consistently initialize and stabilize their numerical solution. In this thesis, we review a fast prolongation method to find hidden constraints, and apply it to systems from MapleSim models. Our symbolic numeric prolongation method avoids the unstable eliminations of exact approaches, and applies to square systems (i.e. systems having the same number of equations and dependent variables). The method is successful provided the prolongations have a block structure, which is efficiently uncovered by Linear Programming. Constrained mechanical systems generated by MapleSim are used to demonstrate the power of the approach. The geometry of the constraints, regarded as the solution set of a positive dimensional polynomial system, is determined by using the new tools of numerical algebraic geometry. We used Bertini, a global homotopy continuation solver, for this purpose. In particular Bertini determines consistent initial conditions on the constraints. These conditions, together with the block structure and an efficient Maple interface enable the efficient numerical solution of the system by standard ODE methods.



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