Mudassir Shams^1,*, Naila Rafiq², Nazir Ahmad Mir^1,2, Babar Ahmad³, Saqib Abbasi¹, Mutee-Ur-Rehman Kayani¹

Computer Systems Science and Engineering, Vol.36, No.3, pp. 493-507, 2021, DOI:10.32604/csse.2021.014476

Abstract In this research article, we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously. These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3. Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3. Using computer algebra system Mathematica, we find the lower bound of the convergence order and verify it theoretically. Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB (R2011b), to present the global convergence properties of inverse simultaneous iterative… 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 >

Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Muhammad Rafiq⁶, Mairaj Bibi⁷, Muhammad Mohsin⁸

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 201-215, 2021, DOI:10.32604/cmes.2021.012111

Abstract Nonlinear stochastic modelling plays an important character in the different fields of sciences such as environmental, material, engineering, chemistry, physics, biomedical engineering, and many more. In the current study, we studied the computational dynamics of the stochastic dengue model with the real material of the model. Positivity, boundedness, and dynamical consistency are essential features of stochastic modelling. Our focus is to design the computational method which preserves essential features of the model. The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature. Analysis and comparison were explored in favour of convergence. Also, we… More >

Tianhong Pan^1,*, Ying Song², Shan Chen²

Intelligent Automation & Soft Computing, Vol.26, No.5, pp. 934-946, 2020, DOI:10.32604/iasc.2020.010125

Abstract The Wiener model is widely used in industrial processes. It is composed of a linear dynamic block and a nonlinear static block. Estimating the Wiener model is challenging because of the diversity of static nonlinear functions and the immeasurableness of intermediate signals owing to the series structure of the Wiener model. Existing optimization algorithms cannot satisfy the requirements of accuracy and efficiency of identification and often lose into a local optimum. Herein, a modified Brain Storm Optimization (mBSO) is proposed to estimate the parameters of the Wiener model. Many different combinations of individuals from intra or extra-groups ensure the diversity… More >

Obadah Said Solaiman, Ishak Hashim^*

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1427-1444, 2021, DOI:10.32604/cmc.2020.012610

Abstract In this paper, we propose a fifth-order scheme for solving systems of nonlinear equations. The convergence analysis of the proposed technique is discussed. The proposed method is generalized and extended to be of any odd order of the form 2n − 1. The scheme is composed of three steps, of which the first two steps are based on the two-step Homeier’s method with cubic convergence, and the last is a Newton step with an appropriate approximation for the derivative. Every iteration of the presented method requires the evaluation of two functions, two Fréchet derivatives, and three matrix inversions. A comparison… More >

Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Kamaledin Abodayeh¹, Muhammad Rafiq⁶, Mairaj Bibi⁷

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1121-1137, 2021, DOI:10.32604/cmc.2020.012070

Abstract Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic… More >

Guorong Cui, Hao Li, Yachuan Zhang, Rongjing Bu, Yan Kang^*, Jinyuan Li, Yang Hu

Journal of Quantum Computing, Vol.2, No.2, pp. 85-95, 2020, DOI:10.32604/jqc.2020.09717

Abstract The traditional K-means clustering algorithm is difficult to determine the cluster number, which is sensitive to the initialization of the clustering center and easy to fall into local optimum. This paper proposes a clustering algorithm based on self-organizing mapping network and weight particle swarm optimization SOM&WPSO (Self-Organization Map and Weight Particle Swarm Optimization). Firstly, the algorithm takes the competitive learning mechanism of a self-organizing mapping network to divide the data samples into coarse clusters and obtain the clustering center. Then, the obtained clustering center is used as the initialization parameter of the weight particle swarm optimization algorithm. The particle position… More >

Chang Su^1,2, Qiangqiang Zheng^3,*, Wukun Zhao⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.16, No.5, pp. 947-960, 2020, DOI:10.32604/fdmp.2020.09676

Abstract In this research, the dynamics of wet spray nozzles with different geometries, used to accelerate shotcrete, are investigated on the basis of a suitable three-dimensional mathematical model and related numerical method. Simulations have been conducted in the frame of the SIMPLEC algorithm. The k-ε turbulence model has been used to account for turbulent effects. The study shows that when the angle of the convergent section is less than 3°, it has a scarce effect on the dynamics of the jet of shotcrete; with the increase of the convergence angle, the shotcrete jet velocity decreases and the nozzle wear increases; when… More >

Yasir Mehmood, Waseem Shahzad

Intelligent Automation & Soft Computing, Vol.25, No.1, pp. 91-103, 2019, DOI:10.31209/2018.100000017

Abstract Particle swarm optimization (PSO) algorithm is a global optimization technique that is used to find the optimal solution in multimodal problems. However, one of the limitation of PSO is its slow convergence rate along with a local trapping dilemma in complex multimodal problems. To address this issue, this paper provides an alternative technique known as ACPSO algorithm, which enables to adopt a new simplified velocity update rule to enhance the performance of PSO. As a result, the efficiency of convergence speed and solution accuracy can be maximized. The experimental results show that the ACPSO outperforms most of the compared PSO… More >

Ali Raza¹, Muhammad Rafiq², Nauman Ahmed³, Ilyas Khan^{4, *}, Kottakkaran Sooppy Nisar⁵, Zafar Iqbal³

CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 263-278, 2020, DOI:10.32604/cmc.2020.011289

Abstract In this manuscript, we consider a stochastic smoking epidemic model from behavioural sciences. Also, we develop a structure preserving numerical method to describe the dynamics of stochastic smoking epidemic model in a human population. The structural properties of a physical system include positivity, boundedness and dynamical consistency. These properties play a vital role in non-linear dynamics. The solution for nonlinear stochastic models necessitates the conservation of these properties. Unfortunately, the aforementioned properties of the model have not been restored in the existing stochastic methods. Therefore, it is essential to construct a structure preserving numerical method for a reliable analysis of… More >