H. S. Shukla¹, Mohammad Tamsir¹, Vineet K. Srivastava², Jai Kumar³

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.103.001

Abstract The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency More >

W.M. Abd- Elhameed^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 159-185, 2014, DOI:10.3970/cmes.2014.101.159

Abstract This paper is concerned with developing two new algorithms for direct solutions of linear and nonlinear sixth-order two point boundary value problems. These algorithms are based on the application of the two spectral methods namely, collocation and Petrov-Galerkin methods. The suggested algorithms are completely new and they depend on introducing a novel operational matrix of derivatives which is expressed in terms of the well-known harmonic numbers. The basic idea for the suggested algorithms rely on reducing the linear or nonlinear sixth-order boundary value problem governed by its boundary conditions to a system of linear or More >

F. Yang¹, C.L. Fu², X.X. Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 19-29, 2014, DOI:10.3970/cmes.2014.100.019

Abstract Numerical differentiation is a classical ill-posed problem. The generalized Tikhonov regularization method is proposed to solve this problem. The error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Numerical examples are presented to illustrate the validity and effectiveness of this method. More >

MARÍA J. RICO^*1,2, PABLO MATAR^*1,2, O. GRACIELA SCHAROVSKY^1,3

BIOCELL, Vol.36, No.2, pp. 91-95, 2012, DOI:10.32604/biocell.2012.36.091

Abstract We have already shown that IL-10 plays an important role in immunosuppression and metastatic dissemination in the rat B-cell lymphoma L-TACB model. It was suggested that the up-regulation of IL10 production and IL-10 receptor (IL-10R) expression would be part of the transition from primary tumor to metastatic phenotype and that IL-10, besides its immunosuppressive activity, may act as a growth factor for metastatic L-TACB cells. The treatment of L-TACB-bearing rats with a single low-dose cyclophosphamide decreased IL-10 production, reverted immunosuppression and induced the immunologic rejection of tumor metastasis without any effect on primary tumor growth.… More >

D. Soares Jr.¹, V. Sladek², J. Sladek², M. Zmindak³, S. Medvecky³

CMC-Computers, Materials & Continua, Vol.27, No.2, pp. 101-127, 2012, DOI:10.32604/cmc.2012.027.101

Abstract This work proposes a modified procedure, based on analytical integrations, to analyse poroelastic models discretized by time-domain Meshless Local Petrov-Galerkin formulations. In this context, Taylor series expansions of the incognita fields are considered, and the related integrals of the meshless formulations are solved analytically, rendering a so called modified methodology. The work is based on the u-p formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the interstitial fluid pore pressures. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient More >

A.E. Martínez-Castro¹, I.H. Faris¹, R. Gallego¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 177-206, 2012, DOI:10.3970/cmes.2012.087.177

Abstract In this paper, the identification of hidden defects inside a three-dimen -sional layer is set as an Identification Inverse Problem. This problem is solved by minimizing a cost functional which is linearized with respect to the volume defects, leading to a procedure that requires only computations at the host domain free of defects. The cost functional is stated as the misfit between experimental and computed displacements and spherical and/or ellipsoidal cavities are the defects to locate. The identification of these cavities is based on the measured displacements at a set of points due to time-harmonic… More >

Y.C. Shiah¹, C. L. Tan², C.Y. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 1-22, 2012, DOI:10.3970/cmes.2012.087.001

Abstract The fundamental solution, or Green's function, for 3D anisotropic elastostatics as derived by Ting and Lee (1997) [Q.J. Mech. Appl. Math.; 50: 407-426] is one that is fully explicit and algebraic in form. It has, however, only been utilized in boundary element method (BEM) formulations quite recently even though it is relatively straightforward and direct to implement. This Green's function and its derivatives are necessary items in this numerical analysis technique. By virtue of the periodic nature of the angles when it is expressed in the spherical coordinate system, the present authors have very recently… More >

H. Çerdik Yaslan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 29-38, 2012, DOI:10.3970/cmes.2012.086.029

Abstract This paper presents the approximate analytical solutions to the time fractional differential equations of elasticity for 3D quasicrystals with initial conditions. These equations are written in the form of a vector partial differential equation of the second order. The time fractional vector partial differential equations with initial conditions are solved by variational iteration method (VIM). The fractional derivatives are described in the Caputo sense. Numerical example shows that the proposed method is quite effective and convenient for solving kinds of time fractional system of partial differential equations. More >

Yiming Chen, Mingxu Yi, Chen Chen, Chunxiao Yu

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 639-654, 2012, DOI:10.3970/cmes.2012.083.639

Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of space-time fractional convection-diffusion equation with variable coefficients. This method combines the definition of fractional derivatives with some properties of Bernstein polynomials and are dispersed the coefficients efficaciously. The main characteristic behind this method is that the original problem is translated into a Sylvester equation. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples show that the method is effective. More >

H.B. Chen

The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.4, pp. 105-106, 2011, DOI:10.3970/icces.2011.020.105

Abstract The calculation of field values and their derivatives near the domain boundary through the boundary element method (BEM) will meet the nearly singularity problem, i.e. the boundary layer effect problem. The tangential derivatives of field values on the boundary often meet an obvious deduction of calculation accuracy. An effective algorithm was proposed by Chen et al. [1,2] to treat these two problems in the same time in elastic BEM and it was recently extended to calculate the second derivative values in potential problem [3]. This algorithm is based on the regularized formulations and is now More >