A new approach to numerical solutions in the linear stability problem of non-newtonian fluids

摘要

A new approach, based on Chebyshev tau-QZ algorithm, quasi-Newton technique, and minimum optimization routine, to the numerical solutions of the nonlinear eigenvalue problem, arising in the linear stability analysis of non-Newtonian fluids heated from below, is presented in this paper. The advantages of our approach are that the resolution of the nonlinear eigenvalue problem is changed into a search algorithm, and the calculations of both neutral stability and overstability can be unified in a single code. Numerical results show that our solutions are in excellent agreement with those of Ref. [1].