Abstract
Abstract An integration algorithm is presented for the numerical solution of a linear, sixth-order eigenvalue problem that is associated with hydrodynamic stability of viscous flow between rotating planes. The solution method approximates the highest derivative of the eigensolutions D 6 phi(y) by passing a third-degree polynomial through three backward points and one forward point. Formulas for the lower derivatives are obtained by integration of the polynomial approximation. Linearity of the differential operator results in an explicit form for the highest derivative at the forward mesh point; a similar, two-point algorithm is used to start the computations. Neutrally stable eigensolutions associated with vortex instability of Taylor's type have been calculated for plane Couette and Poiseuille flow in a rotating system; these solutions agreed well with accepted solutions found by series-expansion methods.
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