The approach set out in this thesis couples partial differential equations for electromagnetic devices - modeled by Maxwell's equations -, to differential-algebraic equations, which describe basic circuit elements including memristors and the circuit's topology.
First, Maxwell's equations are spatially discretized and a potential formulation is derived, the coupled system is then formulated as a differential-algebraic equation with a properly stated leading term and analyzed. Topological and modeling conditions are presented to guarantee the tractability index of these differential-algebraic equations to be no greater than two.
Finally, local solvability, perturbation results and an algorithm to calculate consistent initializations are derived for a general class of differential-algebraic equations with a properly stated leading term having tractability index-2.
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