TY - EJOU AU - Liu, Chein-Shan AU - Atluri, Satya N. TI - A Novel Fictitious Time Integration Method for Solving the Discretized Inverse Sturm-Liouville Problems, For Specified Eigenvalues T2 - Computer Modeling in Engineering \& Sciences PY - 2008 VL - 36 IS - 3 SN - 1526-1506 AB - 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. Then, we use a fictitious time integration method (FTIM) developed by Liu and Atluri (2008), to find the potential function, impedance function or weighting function, in a discretized manner. Numerical examples are presented to show that the Lie-group and FTIM methods have a significantly improved accuracy, along with ease of numerical implementation. The numerical examples also include the inverse problem of determining the material properties and cross-sectional area of a tapered rod undergoing axial vibrations, when the eigen-frequencies are specified. KW - Inverse Sturm-Liouville problem KW - Eigenvalues KW - Eigenfunctions KW - Lie-group method KW - Lie-group shooting method (LGSM) KW - Fictitious time integration method (FTIM) KW - Inverse problem of a vibrating rod for specified frequencies DO - 10.3970/cmes.2008.036.261