The presented above example is very simple. The solution algorithm becomes much more complicated when nonlinear devices such as diodes or transistors and charge-storage components such as capacitors are included in the circuit. Both nonlinear and charge-storage components must be reduced to simplified equivalent circuits before being entered into resolution matrix. These simplification are necessary because system matrices only accept linear I-V relationships.

The system matrices are composed from three arrays: the conductance array representing the values inverse of the resistance values, the voltage array and the current array. For a system built of resistors being linear components, the conductance array remains constant for the duration of the simulation.

G * V = I

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