Home / Journals / CMES / Vol.102, No.2, 2014
Table of Content
  • Open Access

    ARTICLE

    Collocation Methods to Solve Certain Hilbert Integral Equation with Middle Rectangle Rule

    Jin Li1,2, De-hao Yu3,4
    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 103-126, 2014, DOI:10.3970/cmes.2014.102.103
    Abstract The generalized composite middle rectangle rule for the computation of Hilbert integral is discussed. The pointwise superconvergence phenomenon is presented, i.e., when the singular point coincides with some a priori known point, the convergence rate of the rectangle rule is higher than what is global possible. We proved that the superconvergence rate of the composite middle rectangle rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. By choosing the superconvergence point as the collocation points, a collocation scheme for solving the relevant Hilbert integral equation is presented and an error estimate is… More >

  • Open Access

    ARTICLE

    A Wavelet Method for the Solution of Nonlinear Integral Equations with Singular Kernels

    Jizeng Wang1,2, Lei Zhang1, Youhe Zhou1
    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 127-148, 2014, DOI:10.3970/cmes.2014.102.127
    Abstract In this paper, we propose an efficient wavelet method for numerical solution of nonlinear integral equations with singular kernels. The proposed method is established based on a function approximation algorithm in terms of Coiflet scaling expansion and a special treatment of boundary extension. The adopted Coiflet bases in this algorithm allow each expansion coefficient being explicitly expressed by a single-point sampling of the function, which is crucially important for dealing with nonlinear terms in the equations. In addition, we use the technique of integration by parts to transform the original integral equations with non-smooth or singular kernels into regular ones… More >

  • Open Access

    ARTICLE

    Numerical Analysis for the Mooring System with Nonlinear Elastic Mooring Cables

    Z.W. Wu1, J.K. Liu1, Z.Q. Liu1,2, Z.R. Lu1
    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 149-168, 2014, DOI:10.3970/cmes.2014.102.149
    Abstract This paper presents numerical analysis for the mooring system with nonlinear elastic mooring cables. The equation of motion for nonlinear elastic mooring cable is established by utilizing finite element method. A marine mooring system of floating rectangular box with nonlinear elastic cables is taken as an illustrative example. The dynamic analysis, static analysis, and uniformity analysis are carried out for the polyester mooring system and the results are compared with those of the steel wire and the chain mooring system. Results from the present study can provide valuable recommendations for the design and construction of the mooring system with nonlinear… More >

  • Open Access

    ARTICLE

    A Wavelet Method for Solving Bagley-Torvik Equation

    Xiaomin Wang1,2
    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 169-182, 2014, DOI:10.3970/cmes.2014.102.169
    Abstract In this paper, an efficient and robust wavelet Laplace inversion method of solving the fractional differential equations is proposed. Such an inverse function can be applied to any reasonable function categories and it is not necessary to know the properties of original function in advance. As an example, we have applied the proposed method to the solution of the Bagley–Torvik equations and Numerical examples are given to demonstrate the efficiency and accuracy of the proposed. More >

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