CMES-Vol. 100, No. 6, 2014

Open Access

ARTICLE

An Artificial Boundary Method for Burgers’ Equation in the Unbounded Domain
Quan Zheng^1,2, Lei Fan¹, Xuezheng Li¹
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 445-461, 2014, DOI:10.3970/cmes.2014.100.445
Abstract In this paper, we construct a numerical method for one-dimensional Burgers’ equation in the unbounded domain by using artificial boundary conditions. The original problem is converted by Hopf-Cole transformation to the heat equation in the unbounded domain, the latter is reduced to an equivalent problem in a bounded computational domain by using two artificial integral boundary conditions, a finite difference method with discrete artificial boundary conditions is established by using the method of reduction of order for the last problem, and thereupon the numerical solution of Burgers’ equation is obtained. This artificial boundary method is More >

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ARTICLE

Solution of Two-Dimensional Viscous Flow in a Rectangular Domain by the Modified Decomposition Method
Lei Lu^1,2,3, Jun-Sheng Duan², Long-Zhen Fan¹
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 463-475, 2014, DOI:10.3970/cmes.2014.100.463
Abstract In this paper, the modified decomposition method (MDM) for solving the nonlinear two-dimensional viscous flow equations is presented. This study investigates the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions. We first transform the original two-dimensional viscous flow problem into an equivalent fourth-order boundary value problem (BVP), then solve the problem by the MDM. The figures and tables clearly show high accuracy of the method to solve two-dimensional viscous flow. More >

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Static, Free Vibration and Buckling Analysis of Functionally Graded Beam via B-spline Wavelet on the Interval and Timoshenko Beam Theory
Hao Zuo^1,2, Zhi-Bo Yang^1,2,3, Xue-Feng Chen^1,2, Yong Xie⁴, Xing-Wu Zhang^1,2, Yue Liu⁵
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 477-506, 2014, DOI:10.3970/cmes.2014.100.477
Abstract The application of B-spline wavelet on the interval (BSWI) finite element method for static, free vibration and buckling analysis in functionally graded (FG) beam is presented in this paper. The functionally graded material (FGM) is a new type of heterogeneous composite material with material properties varying continuously throughout the thickness direction according to power law form in terms of volume fraction of material constituents. Different from polynomial interpolation used in traditional finite element method, the scaling functions of BSWI are employed to form the shape functions and construct wavelet-based elements. Timoshenko beam theory and Hamilton’s… More >

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ARTICLE

Solving the Lane–Emden–Fowler Type Equations of Higher Orders by the Adomian Decomposition Method
Abdul-Majid Wazwaz¹, R,olph Rach², Lazhar Bougoffa³, Jun-Sheng Duan^{4, 5}
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 507-529, 2014, DOI:10.3970/cmes.2014.100.507
Abstract In this paper, we construct the Lane–Emden–Fowler type equations of higher orders. We study the linear and the nonlinear Lane–Emden–Fowler type equations of the third and fourth orders, where other forms can be treated in a similar manner. We use the systematic Adomian decomposition method to handle these types of equations with specified initial conditions. We confirm that the Adomian decomposition method provides an efficient algorithm for exact and approximate analytic solutions of these equations. We corroborate this study by investigating several numerical examples that emphasize initial value problems. More >

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