CMES-Vol. 99, No. 2, 2014

Open Access

ARTICLE

Numerical Solution of Fractional Fredholm-Volterra Integro-Differential Equations by Means of Generalized Hat Functions Method
Baofeng Li ¹
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 105-122, 2014, DOI:10.3970/cmes.2014.099.105
Abstract In this paper, operational matrix method based on the generalized hat functions is introduced for the approximate solutions of linear and nonlinear fractional integro-differential equations. The fractional order generalized hat functions operational matrix of integration is also introduced. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations. In addition, the method is presented with error analysis. Numerical examples are included to demonstrate the validity and applicability of the approach. More >

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ARTICLE

A Double Iteration Process for Solving the Nonlinear Algebraic Equations, Especially for Ill-posed Nonlinear Algebraic Equations
Weichung Yeih^1,2, I-Yao Chan¹, Cheng-Yu Ku¹, Chia-Ming Fan¹, Pai-Chen Guan³
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 123-149, 2014, DOI:10.3970/cmes.2014.099.123
Abstract In this paper, a novel double iteration process for solving the nonlinear algebraic equations is developed. In this process, the outer iteration controls the evolution path of the unknown vector x in the selected direction u which is determined from the inner iteration process. For the inner iteration, the direction of evolution u is determined by solving a linear algebraic equation: B^TBu = B^TF where B is the Jacobian matrix, F is the residual vector and the superscript ''T'' denotes the matrix transpose. For an ill-posed system, this linear algebraic equation is very difficult to solve since the resulting… More >

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Pore-Scale Modeling of Navier-Stokes Flow in Distensible Networks and Porous Media
Taha Sochi¹
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 151-168, 2014, DOI:10.3970/cmes.2014.099.151
Abstract In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network of interconnected distensible ducts representing, for instance, blood vasculature or deformable porous media. A previously derived analytical expression correlating boundary pressures to volumetric flow rate in compliant tubes for a pressure-area constitutive elastic relation has been used to represent the underlying flow model. Comparison to a preceding equivalent method, the one-dimensional Navier-Stokes finite element, was made and the More >

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Solving the Cauchy Problem of the Nonlinear Steady-state Heat Equation Using Double Iteration Process
Weichung Yeih^1,2, I-Yao Chan¹, Chia-Ming Fan¹, Jiang-Jhy Chang¹, Chein-Shan Liu³
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 169-194, 2014, DOI:10.3970/cmes.2014.099.169
Abstract In this paper, the Cauchy inverse problem of the nonlinear steady-state heat equation is studied. The double iteration process is used to tackle this problem in which the outer loop is developed based on the residual norm based algorithm (RNBA) while the inner loop determines the evolution direction and the modified Tikhonov's regularization method (MTRM) developed by Liu (Liu, 2012) is adopted. For the conventional iteration processes, a fixed evolution direction such as F, B⁻¹F, B^TF or αF+(1-α)B^TF is used where F is the residual vector, B is the Jacobian matrix, the superscript '-1' denotes the inverse, the… More >

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