High-Precision Methods in Eigenvalue Problems and Their ApplicationsThis book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high |
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High-Precision Methods in Eigenvalue Problems and Their Applications Leonid D. Akulenko Limited preview - 2004 |
High-Precision Methods in Eigenvalue Problems and Their Applications Leonid D. Akulenko,Sergei V. Nesterov No preview available - 2004 |
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½ ½ ¼µ ¾ ¾ A₁ accelerated convergence algorithm of accelerated analytical approximate solution assumed asymptotic basis beam boundary conditions boundary value problem calculations Cauchy problem Chapter coefficients computational consider const constant constructed corresponding cross-section curves density dependence described determined differential equations eigenfrequencies eigenfunctions eigenvalue problem eigenvalues and eigenfunctions elastic elliptic expressions formulas free vibrations frequencies inequality inhomogeneous integral equation interval iteration linear lower bound Mathieu equation membrane method of accelerated numerical-analytical method obtain the following orthogonal parameter ɛ perturbation method procedure Rayleigh principle Rayleigh-Ritz method refined value relative error respect root sagittary function Section small parameter solving Sturm-Liouville problem subsequent eigenvalues sufficiently small test function Theorem theory u₁ un(x upper bound V₁ variables variational vibration modes vibration shapes yields zero πη
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