Arif Amirov¹, Fikret Gölgeleyen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 179-192, 2010, DOI:10.3970/cmes.2010.065.179

Abstract In this work, we derive the solvability conditions for an inverse problem for the kinetic equation and develop a new symbolic algorithm to obtain the approximate solution of the problem. The computational experiments show that proposed method provides highly accurate numerical solutions even subjecting to a large noise in the given data. More >

Mustafa Yidiz¹, Bayram Heydarov², İsmet Gölgeleyen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.3, pp. 255-264, 2010, DOI:10.3970/cmes.2010.062.255

Abstract We investigate the solvability of an inverse problem for the non-stationary general kinetic equation. We also obtained the approximate solution of this problem by using symbolic computation. A comparison between the approximate solution and the exact solution of the problem is presented. More >

Arif Amirov¹, Zekeriya Ustaoglu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 283-300, 2009, DOI:10.3970/cmes.2009.054.283

Abstract We present the solvability of a two space dimensional coefficient inverse problem for a transport-like equation and investigate the approximate solution of this problem with the use of centered difference formulas and a symbolic approximation method. Since this inverse problem is overdetermined, which is the main difficulty in studying of its solvability, it is replaced by a related determined one by using some extension of the class of unknown functions. More >

Mustafa Yildiz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.2, pp. 141-154, 2009, DOI:10.3970/cmes.2009.045.141

Abstract The solvability conditions of an inverse problem for the non-stationary kinetic equation is formulated and a new numerical method is developed to obtain the approximate solution of the problem. A comparison between the approximate solution and the exact solution of the problem is presented. More >

Shang Zhang^{1, *}, Seyedmehdi Karimi², Shahaboddin Shamshirband^{3, 4, *}, Amir Mosavi^5,6

CMC-Computers, Materials & Continua, Vol.58, No.2, pp. 567-583, 2019, DOI:10.32604/cmc.2019.02795

Abstract In the process of eliminating variables in a symbolic polynomial system, the extraneous factors are referred to the unwanted parameters of resulting polynomial. This paper aims at reducing the number of these factors via optimizing the size of Dixon matrix. An optimal configuration of Dixon matrix would lead to the enhancement of the process of computing the resultant which uses for solving polynomial systems. To do so, an optimization algorithm along with a number of new polynomials is introduced to replace the polynomials and implement a complexity analysis. Moreover, the monomial multipliers are optimally positioned to multiply each of the… More >