Analytic continuation and resonance-free regions for Sturm--Liouville potentials with power decay
Journal of Computational and Applied Mathematics - On the occasion of the 65th birthday of Prof. Michael Eastham
A Legendre spectral element method for eigenvalues in hydrodynamic stability
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Spectral methods in linear stability. Applications to thermal convection with variable gravity field
Applied Numerical Mathematics
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This paper gives the analysis and numerics underlying a shooting method for approximating the eigenvalues of non--self-adjoint Sturm--Liouville problems. We consider even order problems with (equally divided) separated boundary conditions. The method can find the eigenvalues in a rectangle and in a left half-plane. It combines the argument principle with the compound matrix method (using the Magnus expansion). In some cases the computational cost of compound matrices can be reduced by transforming to a second order vector Sturm--Liouville problem. We study the asymptotics of the solutions of the ODE for large absolute values of the eigenvalue parameter in order to calculate the eigenvalues in a left half-plane. The method is applied to the Orr--Sommerfeld equation and other examples.