Numerical Solution of Non--Self-Adjoint Sturm--Liouville Problems and Related Systems

DOI10.1137/S0036142999358743zbMath1001.34020MaRDI QIDQ2706390

Leon Greenberg, Marco Marlettta

Publication date: 19 March 2001

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

contour integralOrr-Sommerfeld equationshooting methodargument principleMagnus methodcompound matrix methodhigher-order Sturm-Liouville problemnumerical eigenvalue computation

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (14)

Least-Squares Spectral Methods for ODE Eigenvalue Problems ⋮ Computing the spectrum of non-self-adjoint Sturm-Liouville problems with parameter-dependent boundary conditions ⋮ An efficient numerical technique for estimating eigenvalues of second-order non-self-adjoint Sturm-Liouville problems ⋮ Inverse nodal problems for the Sturm-Liouville operator with nonlocal integral conditions ⋮ Numerical solution of vector Sturm-Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter ⋮ Grassmannian spectral shooting ⋮ Evaluating the Evans function: Order reduction in numerical methods ⋮ A Legendre spectral element method for eigenvalues in hydrodynamic stability ⋮ Spectral methods in linear stability. Applications to thermal convection with variable gravity field ⋮ Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains ⋮ Numerical methods for higher order Sturm-Liouville problems ⋮ Numerical evaluation of the Evans function by Magnus integration ⋮ Analytic continuation and resonance-free regions for Sturm-Liouville potentials with power decay ⋮ Fast and accurate calculations of fourth-order non-self-adjoint Sturm-Liouville eigenvalues for problems in physics and engineering

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