An optimal arrangement of simultaneous linearized equations for general systems of interlinked, multistoged separators

The simultaneous solution of all the equations for a general system of interlinked, multistaged separators is considered. The interlinks may be simple streams or reciprocal streams, and a particular separator may have bypassing streams (for example, pumparounds). Algorithms are developed that automatically arrange the linearized equations so that for a Newton‐Raphson type of solution procedure using, for example, the Naphtali‐Sandholm technique, a minimum or nearly minimum number of nonzero blocks occur outside the tridiagonal band so that computational memory and time requirements are minimized. The nonzero and nonidentity blocks are stored in a single vector of variable dimension.