CMES-Vol. 99, No. 5, 2014

Open Access

ARTICLE

A New Approach to a Fuzzy Time-Optimal Control Problem
Ş. Emrah Amrahov¹, N. A. Gasilov², A. G. Fatullayev²
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 351-369, 2014, DOI:10.3970/cmes.2014.099.351
Abstract In this paper, we present a new approach to a time-optimal control problem with uncertainties. The dynamics of the controlled object, expressed by a linear system of differential equations, is assumed to be crisp, while the initial and final phase states are fuzzy sets. We interpret the problem as a set of crisp problems. We introduce a new notion of fuzzy optimal time and transform its calculation to two classical time-optimal control problems with initial and final sets. We examine the proposed approach on an example which is a problem of fuzzy control of mathematical More >

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ARTICLE

An LGDAE Method to Solve Nonlinear Cauchy Problem Without Initial Temperature
Chein-Shan Liu ¹
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 371-391, 2014, DOI:10.3970/cmes.2014.099.371
Abstract We recover an unknown initial temperature for a nonlinear heat conduction equation u_t(x,t) = u_xx(x,t) + H(x,t,u,u_x), under the Cauchy boundary conditions specified on the left-boundary. The method in the present paper transforms the Cauchy problem into an inverse heat source problem to find F(x) in T_t(x,t) = T_xx(x,t) + H + F(x). By using the GL(N,R) Lie-group differential algebraic equations (LGDAE) algorithm to integrate the numerical method of lines discretized equations from sideways heat equation, we can fast recover the initial temperature and two boundary conditions on the right-boundary. The accuracy and efficiency are confirmed by comparing the More >

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Non-Singular Method of Fundamental Solutions based on Laplace decomposition for 2D Stokes flow problems
E. Sincich¹, B. Šarler^1,2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 393-415, 2014, DOI:10.3970/cmes.2014.099.393
Abstract In this paper, a solution of a two-dimensional (2D) Stokes flow problem, subject to Dirichlet and fluid traction boundary conditions, is developed based on the Non-singular Method of Fundamental Solutions (NMFS). The Stokes equation is decomposed into three coupled Laplace equations for modified components of velocity, and pressure. The solution is based on the collocation of boundary conditions at the physical boundary by the fundamental solution of Laplace equation. The singularities are removed by smoothing over on disks around them. The derivatives on the boundary in the singular points are calculated through simple reference solutions. More >

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Singular Boundary Method: Three Regularization Approaches and Exterior Wave Applications
Zhuo-Jia Fu¹, Wen Chen^1,2, Jeng-Tzong Chen³, Wen-Zhen Qu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 417-443, 2014, DOI:10.3970/cmes.2014.099.417
Abstract This study investigates the singular boundary method (SBM) with three regularization approaches for solving 2D and 3D exterior wave problems. The singular boundary method is a recent meshless boundary collocation method, which introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. Recently, three approaches, the inverse interpolation technique (IIT), the semi-analytical technique with boundary IIT (SAT1) and the semi-analytical technique with integral mean value (SAT2), have been proposed to determine the source intensity factors for removing the singularities of Helmholtz fundamental solutions at origin. This study compares numerical accuracy… More >

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