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Solution of ODEs and Eigenvalue Problems with a Chebyshev Polynomial Spectral Method
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| Organization: | University of Notre Dame |
| Department: | Department of Chemical Engineering |
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0210-205
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1999-05-18
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This notebook demonstrates the Orszag-tau (a modification of the Galerkin) spectral method for a simple ODE and an ODE eigenvalue problem. It is intended as a first introduction to solving these problems with a spectral numerical method.
Reference: S. A. Orszag (1971) "Accurate solution of the Orr-Sommerfeld stability equation", Journal of Fluid Mechanics, 50 pp 689-703.
The coefficients of the algebraic equations are computed directly from the orthogonality properties of the Chebyshev polynomials using orthogonality.
Reference: R. Miesen and B. J. Boersma (1995) "Hydrodynamic stability of a sheared liquid film", Journal of Fluid Mechanics, 301 pp 175-202.
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Tau-spectral method, numerical eigenvalue problem, spectral method
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| spectral_ode_eigens.nb (764.8 KB) - Mathematica notebook |
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