CMES-Vol. 97, No. 5, 2014

Open Access

ARTICLE

Numerical Solution for a Class of Linear System of Fractional Differential Equations by the Haar Wavelet Method and the Convergence Analysis
Yiming Chen¹, Xiaoning Han¹, Lechun Liu ¹
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 391-405, 2014, DOI:10.3970/cmes.2014.097.391
Abstract In this paper, a class of linear system of fractional differential equations is considered. It has been solved by operational matrix of Haar wavelet method which converts the problem into algebraic equations. Moreover the convergence of the method is studied, and three numerical examples are provided to demonstrate the accuracy and efficiency. More >

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ARTICLE

Flexural Wave Dispersion in Bi-material Compound Solid and Hollow Circular Cylinders
S.D. Akbarov ^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 407-424, 2014, DOI:10.3970/cmes.2014.097.407
Abstract Flexural wave dispersion in a bi-material solid and hollow circular cylinders is investigated with the use of the three-dimensional linear theory of elastodynamics. It is assumed that on the interface surface of the cylinders the complete contact conditions satisfy. The analytical solution of the corresponding field equations is presented and, using these solutions, the dispersion equations for the cases under consideration are obtained. The dispersion equations are solved numerically and based on these solutions, dispersion curves are constructed for the concrete selected pairs of materials such as Tungsten (inner cylinder material) + Aluminum (outer cylinder material) and Steel (inner cylinder… More >

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Research on Band Structure of One-dimensional Phononic Crystals Based on Wavelet Finite Element Method
Mao Liu^1,2, Jiawei Xiang¹, Haifeng Gao¹, Yongying Jiang¹, Yuqing Zhou¹, Fengping Li¹
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 425-436, 2014, DOI:10.3970/cmes.2014.097.425
Abstract A wavelet finite element method (WFEM) is developed to analyze the dispersion relation for one-dimensional phononic crystals (1DPCs). In order to calculate the band gaps (BGs) of 1DPCs, the wavelet finite element model is constructed using a slender beam element based on B-spline wavelet on the interval (BSWI). Combining with the Bloch-Floquet theorem and ω(k) technique, the model will be simplified as a simple eigenproblem. The performance of the proposed method has been numerically verified by one numerical example. More >

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ARTICLE

Cauchy Problem for the Heat Equation in a Bounded Domain Without Initial Value
Ji-Chuan Liu¹, Jun-Gang Wang²
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 437-462, 2014, DOI:10.3970/cmes.2014.097.437
Abstract We consider the determination of heat flux within a body from the Cauchy data. The aim of this paper is to seek an approach to solve the onedimensional heat equation in a bounded domain without initial value. This problem is severely ill-posed and there are few theoretic results. A quasi-reversibility regularization method is used to obtain a regularized solution and convergence estimates are given. For numerical implementation, we apply a method of lines to solve the regularized problem. From numerical results, we can see that the proposed method is reasonable and feasible. More >

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