CMES-Vol. 105, No. 5, 2015

Open Access

ARTICLE

A Second-order Time-marching Procedure with Enhanced Accuracy
Delfim Soares Jr.¹
CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.5, pp. 341-360, 2015, DOI:10.3970/cmes.2015.105.341
Abstract In this work, a second-order time-marching procedure for dynamics is discussed, in which enhanced accuracy is enabled. The new technique is unconditionally stable (according to its parameter selection), it has no amplitude decay or overshooting, and it provides reduced period elongation errors. The method is based on displacement-velocity relations, requiring no computation of accelerations. It is efficient, simple and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the proposed technique. As it is described here, the new method has no drawbacks when compared to the Trapezoidal Rule (TR), which is one of… More >

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Finding the Generalized SolitaryWave Solutions within the (G'/G)-Expansion Method
K. Sayevand¹, Yasir Khan², E. Moradi³, M. Fardi⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.5, pp. 361-373, 2015, DOI:10.3970/cmes.2015.105.361
Abstract In this study, the solitary wave solutions for third order equal-width wave-Burgers (EW-Burgers) equation, the second order Bratu and sinh-Bratu type equations will be discussed. The EW-Burgers equation models the propagation of nonlinear and dispersive waves with certain dissipative effects and furthermore the Bratu type problem appears a simplification of the solid fuel ignition model in thermal combustion theory. Our methodology, is investigated by using (G'/G)- expansion method. The obtained results can be extended to the other models. More >

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New Spectral Solutions of Multi-Term Fractional-Order Initial Value ProblemsWith Error Analysis
W. M. Abd- Elhameed^1,2, Y. H. Youssri²
CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.5, pp. 375-398, 2015, DOI:10.3970/cmes.2015.105.375
Abstract In this paper, a new spectral algorithm for solving linear and nonlinear fractional-order initial value problems is established. The key idea for obtaining the suggested spectral numerical solutions for these equations is actually based on utilizing the ultraspherical wavelets along with applying the collocation method to reduce the fractional differential equation with its initial conditions into a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. The convergence and error analysis of the suggested ultraspherical wavelets expansion are carefully discussed. For the sake of testing the proposed algorithm, some numerical examples are considered. The numerical results indicate… More >

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RBFN stochastic coarse-grained simulation method: Part I - Dilute polymer solutions using Bead-Spring Chain models
H.Q. Nguyen¹, C.-D. Tran¹, T. Tran-Cong¹
CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.5, pp. 399-439, 2015, DOI:10.3970/cmes.2015.105.399
Abstract In this paper, dynamic behaviours of dilute polymer solutions of various bead-spring chain models in shear flow are studied using a coarse-grained method based on the Integrated Radial Basis Function Networks (IRBFNs) and stochastic technique. The velocity field governed by the macroscopic conservation equations is determined by the IRBFN-based method, whereas the evolution of configurations of polymer chains governed by the diffusion stochastic differential equations are captured by the Brownian Configuration Field (BCF) approach. The system of micro-macro equations is closed by the Kramers’ expression, which allows for the determination of the polymer stresses in terms of BCF configurations. In… More >

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