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Parallel analog circuits are introduced for the solution of systems of nonlinear algebraic equations and the integration of systems of differential equations. Both simulations using HSPICE and a hardware implementation are presented which show how the circuitry can be used to solve: the power flow and transient analysis problems for power systems, and the simulation of a jet engine. In all cases solutions are obtained in better than real time. The results are comparable in accuracy to digital solutions of the same problems.