Naila Rafiq¹, Saima Akram², Mudassir Shams^3,*, Nazir Ahmad Mir¹

CMC-Computers, Materials & Continua, Vol.69, No.2, pp. 2635-2651, 2021, DOI:10.32604/cmc.2021.018955

Abstract In this research article, we construct a family of derivative free simultaneous numerical schemes to approximate all real zero of non-linear polynomial equation. We make a comparative analysis of the newly constructed numerical schemes with a well-known existing simultaneous method for determining all the distinct real zeros of polynomial equations using computer algebra system Mat Lab. Lower bound of convergence of simultaneous schemes is calculated using Mathematica. Global convergence property of the numerical schemes is presented by taking random starting initial approximation and their convergence history are graphically presented. Some real life engineering applications along with some higher degree polynomials… More >

Obadah Said Solaiman¹, Samsul Ariffin Abdul Karim², Ishak Hashim^1,*

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1951-1962, 2021, DOI:10.32604/cmc.2021.015344

Abstract There are several ways that can be used to classify or compare iterative methods for nonlinear equations, for instance; order of convergence, informational efficiency, and efficiency index. In this work, we use another way, namely the basins of attraction of the method. The purpose of this study is to compare several iterative schemes for nonlinear equations. All the selected schemes are of the third-order of convergence and most of them have the same efficiency index. The comparison depends on the basins of attraction of the iterative techniques when applied on several polynomials of different degrees. As a comparison, we determine… More >

Obadah Said Solaiman, Ishak Hashim^*

Intelligent Automation & Soft Computing, Vol.27, No.2, pp. 379-390, 2021, DOI:10.32604/iasc.2021.015285

Abstract A new iterative technique for nonlinear equations is proposed in this work. The new scheme is of three steps, of which the first two steps are based on the sixth-order modified Halley’s method presented by the authors, and the last is a Newton step, with suitable approximations for the first derivatives appeared in the new scheme. The eighth-order of convergence of the new method is proved via Mathematica code. Every iteration of the presented scheme needs the evaluation of three functions and one first derivative. Therefore, the scheme is optimal in the sense of Kung-Traub conjecture. Several test nonlinear problems… More >

Yuming Chu¹, Naila Rafiq², Mudassir Shams^3,*, Saima Akram⁴, Nazir Ahmad Mir³, Humaira Kalsoom⁵

CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 275-290, 2021, DOI:10.32604/cmc.2020.011907

Abstract In this article, we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations. Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine. Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes, numerical experiments and CPU time-methodology. Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous… More >

Yasunori Yusa¹, Shinobu Yoshimura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.1, pp. 87-104, 2014, DOI:10.3970/cmes.2014.099.087

Abstract To speed up the elastic–plastic analysis of a large-scale model with a crack in which plasticity is observed near the crack, the partitioned coupling method is applied. In this method, the entire analysis model is decomposed into two non-overlapped domains (i.e., global and local domains), and the two domains are analyzed with an iterative method. The cracked local domain is modeled as an elastic–plastic body, whereas the large-scale global domain is modeled as an elastic body. A subcycling technique is utilized for incremental analysis to reduce the number of global elastic analyses. For a benchmark problem with 6 million degrees… More >