Home / Journals / CMES / Vol.84, No.5, 2012
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  • Open Access

    ARTICLE

    On Determination of a Finite Jacobi Matrix from Two Spectra

    Gusein Sh. Guseinov1
    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 405-422, 2012, DOI:10.3970/cmes.2012.084.405
    Abstract In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. More >

  • Open Access

    ARTICLE

    Numerical Solutions of the Symmetric Regularized Long Wave Equation Using Radial Basis Functions

    Ayşe Gül Kaplan1, Yılmaz Dereli
    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 423-438, 2012, DOI:10.3970/cmes.2012.084.423
    Abstract In this study, the nonlinear symmetric regularized long wave equation was solved numerically by using radial basis functions collocation method. The single solitary wave solution, the interaction of two positive solitary waves and the clash of two solitary waves were studied. Numerical results and simulations of the wave motions were presented. Validity and accuracy of the method was tested by compared with results in the literature. More >

  • Open Access

    ARTICLE

    Mode-III Stress Intensity Factors of a Three-Phase Composite with an Eccentric Circular Inclusion

    C.K. Chao1, A. Wikarta1
    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 439-458, 2012, DOI:10.3970/cmes.2012.084.439
    Abstract An analytical solution to a three-phase composite with an eccentric circular inclusion under a remote uniform shear load is given in this work. Mode-III stress intensity factors for an arbitrarily oriented crack embedded in an infinite matrix or a core inclusion are provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation located either in the core inclusion or in the infinite matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack are established by using the screw… More >

  • Open Access

    ARTICLE

    A Simple Collocation Scheme for Obtaining the Periodic Solutions of the Duffing Equation, and its Equivalence to the High Dimensional Harmonic Balance Method: Subharmonic Oscillations

    Hong-Hua Dai1,2, Matt Schnoor2, Satya N. Atluri2
    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 459-498, 2012, DOI:10.3970/cmes.2012.084.459
    Abstract In this study, the harmonic and 1/3 subharmonic oscillations of a single degree of freedom Duffing oscillator with large nonlinearity and large damping are investigated by using a simple point collocation method applied in the time domain over a period of the periodic solution. The relationship between the proposed collocation method and the high dimensional harmonic balance method (HDHB), proposed earlier by Thomas, Dowell, and Hall (2002), is explored. We demonstrate that the HDHB is not a kind of "harmonic balance method" but essentially a cumbersome version of the collocation method. In using the collocation method, the collocation-resulting nonlinear algebraic… More >

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