A practical implementation of spectral methods resistant to the generation of spurious eigenvalues. (English) Zbl 0762.76082
Summary: This work describes a practical way of constructing a spectral representation of linear boundary value problems (BVPs) using a tau method. All BVPs are treated as first-order systems, unlike most implementations which tend to view the problem in terms of a single high- order differential equation. For most applications this formulation will adhere more closely to the natural derivation of the original equations from, for example, a series of conservation laws. The technique is exemplified for Chebyshev polynomials in a variety of real applications, although detailed results are provided for any polynomial basis.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76E05 | Parallel shear flows in hydrodynamic stability |
| 76E20 | Stability and instability of geophysical and astrophysical flows |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
Keywords:
Orr-Sommerfeld equation; convection; porous medium; viscous fluid; linear boundary value problems; tau method; conservation laws; Chebyshev polynomialsReferences:
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