CMES-Vol. 92, No. 4, 2013

Open Access

ARTICLE

Simulation of Natural Convection Influenced by Magnetic Field with Explicit Local Radial Basis Function Collocation Method
K. Mramor¹, R. Vertnik^2,3, B. Šarler^1,3,4,5
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 327-352, 2013, DOI:10.3970/cmes.2013.092.327
Abstract The purpose of the present paper is to extend and explore the application of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of a steady, laminar, natural convection flow, influenced by magnetic field. The problem is defined by coupled mass, momentum, energy and induction equations that are solved in two dimensions by using local collocation with multiquadrics radial basis functions on an overlapping five nodded subdomains and explicit time-stepping. The fractional step method is used to couple the pressure and velocity fields. The considered problem is calculated in a square cavity… More >

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ARTICLE

Wavelet operational matrix method for solving fractional integral and differential equations of Bratu-type
Lifeng Wang¹, Yunpeng Ma¹, Zhijun Meng¹, Jun Huang¹
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 353-368, 2013, DOI:10.3970/cmes.2013.092.353
Abstract In this paper, a wavelet operational matrix method based on the second kind Chebyshev wavelet is proposed to solve the fractional integral and differential equations of Bratu-type. The second kind Chebyshev wavelet operational matrix of fractional order integration is derived. A truncated second kind Chebyshev wavelet series together with the wavelet operational matrix is utilized to reduce the fractional integral and differential equations of Bratu-type to a system of nonlinear algebraic equations. The convergence and the error analysis of the method are also given. Two examples are included to verify the validity and applicability of More >

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Solution of Quadratic Integral Equations by the Adomian Decomposition Method
Shou-Zhong Fu¹, Zhong Wang¹, Jun-Sheng Duan^1,2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 369-385, 2013, DOI:10.3970/cmes.2013.092.369
Abstract Quadratic integral equations are a class of nonlinear integral equations having many important uses in engineering and sciences. In this work we display an efficient application of the Adomian decomposition method to the quadratic integral equations of Volterra type. The analytical approximate solution obtained can be directly inserted into the original equation to verify the accuracy and estimate the error with a computing software. Four numerical examples demonstrate the efficiency of the method. More >

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Flexural wave dispersion in finitely pre-strained solid and hollow circular cylinders made of compressible materials
S. D. Akbarov^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 387-421, 2013, DOI:10.3970/cmes.2013.092.387
Abstract Flexural wave dispersion in finitely pre-stretched (or pre-compressed) solid and hollow, circular cylinders is investigated with the use of the threedimensional linearized theory of elastic waves in initially stressed bodies. It is assumed that the initial strains in the cylinders are homogeneous and correspond to the uniaxial tension, or compression, along their central axes. The elasticity relations of the cylinders’ materials are described by the harmonic potential. 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… More >

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