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Remarks to the numerical treatment of nonselfadjoint eigenvalue problems. (English) Zbl 0880.65030

Bainov, Drumi (ed.) et al., Proceedings of the 3rd international colloquium on numerical analysis, Plovdiv, Bulgaria, August 13–17, 1994. Invited lectures and short communications. Singapore: SCT Publishing, 117-126 (1995).
Summary: For a parameter dependent nonselfadjoint eigenvalue problem with differential equations, which has been transformed into an equivalent matrix eigenvalue problem with infinite dimensions, the parameter space is investigated for regions, where all eigenvalues have nonnegative real parts and regions where there exists a single eigenvalue having a negative real part. The sufficient conditions employed, to guarantee that all eigenvalues of the problem under consideration have nonnegative real parts, is better than a condition used earlier since the boundary line in parameter space obtained by the new condition is very much closer to the boundary line signifying the existence of eigenvalues with a negative real part. As numerical example the plane Orr-Sommerfeld problem is considered, where the basic flow is a linear combination of Poiseuille flow and Couette flow.
For the entire collection see [Zbl 0870.00045].

MSC:

65J10 Numerical solutions to equations with linear operators
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A42 Inequalities involving eigenvalues and eigenvectors
47A75 Eigenvalue problems for linear operators
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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