Chein-Shan Liu1, Satya N. Atluri2
CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.3, pp. 261-286, 2008, DOI:10.3970/cmes.2008.036.261
Abstract The inverse Sturm-Liouville problem finds its applications in the identification of mechanical properties and/or geometrical configurations of a vibrating continuous medium; however, this problem is hard to solve, either theoretically or numerically. Previously, Liu (2008a) has constructed a Lie-group shooting method to determine the eigenvalues, and the corresponding eigenfunctions, for the direct Sturm-Liouville problem. In this study, we are concerned with solving the inverse Sturm-Liouville problem, by developing a Lie-group of SL(2,R) to construct nonlinear algebraic equations (NAEs), when discrete eigenvalues are specified. Our purpose here is to use these NAEs to solve the unknown function in the Sturm-Liouville operator.… More >
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