A modified tau spectral method that eliminated spurious eigenvalues
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems
Applied Numerical Mathematics
Matrix computations (3rd ed.)
Numerical methods for higher order Sturm-Liouville problems
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Numerical Solution of Non--Self-Adjoint Sturm--Liouville Problems and Related Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Spectral methods in linear stability. Applications to thermal convection with variable gravity field
Applied Numerical Mathematics
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A Legendre polynomial-based spectral technique is developed to be applicable to solving eigenvalue problems which arise in linear and nonlinear stability questions in porous media, and other areas of Continuum Mechanics. The matrices produced in the corresponding generalised eigenvalue problem are sparse, reducing the computational and storage costs, where the superimposition of boundary conditions is not needed due to the structure of the method. Several eigenvalue problems are solved using both the Legendre polynomial-based and Chebyshev tau techniques. In each example, the Legendre polynomial-based spectral technique converges to the required accuracy utilising less polynomials than the Chebyshev tau method, and with much greater computational efficiency.