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Numerical solution of eigenvalue problems for partial differential equations with the tau-lines method. (English) Zbl 0626.65109

A hybrid approach is discussed, using the tau method in combination with the method of lines. The authors treat a number of eigenvalue problems defined by partial differential equations with constant and variable coefficients, on rectangular or circular domains and with eigenvalue parameters entering in the equation or in the boundary conditions. Numerical results are presented for the vibrating membrane problem, the Steklov eigenvalue problem for partial differential equations, and the Helmholtz eigenvalue problem in a circular domain. The results are obtained with considerable accuracy. The proposed method is easy to implement on a computer.
Reviewer: E.V.Nicolau

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N40 Method of lines for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74H45 Vibrations in dynamical problems in solid mechanics
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References:

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