On the use of the method of quadrature by differentiation for solving eigenvalue problems in hydrodynamic stability
Abstract
The usefulness of the method of quadrature by differentiation for solving eigenvalue problems in hydrodynamic stability is demonstrated. A numerical example, the Taylor problem, is presented in order to show the efficacy of the method and provide a basis of comparison with other approximate methods (e.g. the Galerkin method). The results were found to be in good agreement with experimental data and it was demonstrated that the method of quadrature by differentiation in comparison with other analytical methods requires no trial and error, no extensive mathematical investigation, and no lengthy computer computations.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- December 1974
- DOI:
- 10.1016/0021-9991(74)90042-4
- Bibcode:
- 1974JCoPh..16..315S
- Keywords:
-
- Couette Flow;
- Eigenvalues;
- Flow Stability;
- Quadratures;
- Taylor Instability;
- Differential Equations;
- Equations Of Motion;
- Incompressible Flow;
- Navier-Stokes Equation;
- Rotating Cylinders;
- Viscous Flow;
- Fluid Mechanics and Heat Transfer