Xuechuan Wang¹, Wei He^1,*, Haoyang Feng¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1263-1294, 2024, DOI:10.32604/cmes.2023.043068

Abstract Although predictor-corrector methods have been extensively applied, they might not meet the requirements of practical applications and engineering tasks, particularly when high accuracy and efficiency are necessary. A novel class of correctors based on feedback-accelerated Picard iteration (FAPI) is proposed to further enhance computational performance. With optimal feedback terms that do not require inversion of matrices, significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts; however, the computational complexities are comparably low. These advantages enable nonlinear engineering problems to be solved quickly and accurately, even with rough initial guesses from elementary predictors.… More > Graphic Abstract

Kamal Shah^1,2, Thabet Abdeljawad^3,4,*, Fahd Jarad⁵, Qasem Al-Mdallal⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1457-1472, 2023, DOI:10.32604/cmes.2023.021523

Abstract This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series… More >

Kamal Shah^1,2, Hafsa Naz², Thabet Abdeljawad^1,3,*, Bahaaeldin Abdalla¹

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 921-941, 2023, DOI:10.32604/cmes.2023.025769

Abstract This research aims to understand the fractional order dynamics of the deadly Nipah virus (NiV) disease. We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system. We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem. By utilizing the Newtonian polynomials interpolation technique, we recall a powerful algorithm to interpret the numerical findings for the aforesaid model. Here, we remark that the said viral infection is caused by an RNA type virus… More > Graphic Abstract

Prem Junsawang¹, Zulqurnain Sabir², Muhammad Asif Zahoor Raja³, Soheil Salahshour⁴, Thongchai Botmart^5,*, Wajaree Weera³

CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 249-263, 2022, DOI:10.32604/cmc.2022.028513

Abstract The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system. The delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator system. Therefore, a stochastic numerical paradigm based artificial neural network (ANN) along with the Levenberg-Marquardt backpropagation (L-MB) neural networks (NNs), i.e., L-MBNNs is proposed to solve the dynamical two-prey and one-predator model. Three different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the L-MBNNs. The statistic measures of these outcomes of… More >

Y. A. Amer¹, Taher A. Bahnasy^2,*

Sound & Vibration, Vol.55, No.3, pp. 191-201, 2021, DOI:10.32604/sv.2021.014358

Abstract An externally excited Duffing oscillator under feedback control is discussed and analyzed under the worst resonance case. Multiple time scales method is applied for this system to find analytic solution with the existence and nonexistence of the time delay on control loop. An appropriate stability analysis is also performed and appropriate choices for the feedback gains and the time delay are found in order to reduce the amplitude peak. Different response curves are involved to show and compare controller effects. In addition, analytic solutions are compared with numerical approximation solutions using Rung-Kutta method of fourth order. More >

Abdulsattar Abdullah Hamad¹, Ahmed S. Al-Obeidi², Enas H. Al-Taiy², Osamah Ibrahim Khalaf³, Dac-Nhuong Le^4,5,*

CMC-Computers, Materials & Continua, Vol.66, No.3, pp. 3311-3327, 2021, DOI:10.32604/cmc.2021.013395

Abstract Synchronization is one of the most important characteristics of dynamic systems. For this paper, the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems. The findings have allowed authors to develop two analytical approaches using the second Lyapunov (Lyp) method and the Gardano method. Since the Gardano method does not involve the development of special positive Lyp functions, it is very efficient and convenient to achieve excessive system SYCR phenomena. Error is overcome by using Gardano and overcoming some problems in Lyp. Thus we get a great investigation into the convergence of error… More >

R. Sampaio¹, C. Soize²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.2, No.4, pp. 93-100, 2007, DOI:10.3970/icces.2007.002.093

Abstract An analysis of the efficiency of the reduced models constructed using the POD-basis and the LIN-basis is presented in nonlinear dynamics for continuous elastic systems discretized by the finite element method. The POD-basis is the basis constructed with the POD method while the LIN-basis is the basis derived from the generalized eigenvalue problem associated with the underlying linear conservative part of the system and usually called the eigenmodes of vibration. The efficiency of the POD-basis or the LIN-basis is related to the speed of convergence in the frequency domain of the solution constructed with the reduced model with respect to… More >

Xuechuan Wang¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.6, pp. 567-585, 2016, DOI:10.3970/cmes.2016.111.567

Abstract This paper compares the variational iteration method (VIM), the Adomian decomposition method (ADM) and the Picard iteration method (PIM) for solving a system of first order nonlinear ordinary differential equations (ODEs). A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM. It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM. The global variational iteration method is briefly reviewed, and further recast into a Local VIM, which is much more convenient… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.4, pp. 375-407, 2014, DOI:10.3970/cmes.2014.098.375

Abstract In this paper we study the nonlinear dynamical system x^·=f(x,t) from a newly developed theory, viewing the time-varying function of sign(||f||²||x||²− 2(f·x)²) = −sign(cos 2θ) as a key factor, where θ is the intersection angle between x and f. It together with sign(cos θ) can reveal the complexity of nonlinear Duffing oscillator and a quadratic ship rolling oscillator. The barcode is formed by plotting sign(||f||²||x||²− 2(f·x)²) with respect to time. We analyze the barcode to point out the bifurcation of subharmonic motions and the range of chaos in the parameter space. The bifurcation diagram obtained by plotting the percentage… More >

T.A. Elgohary^1,2, L. Dong³, J.L. Junkins^2,4, S.N. Atluri^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.3, pp. 249-275, 2014, DOI:10.3970/cmes.2014.100.249

Abstract In this study, we consider Initial Value Problems (IVPs) for strongly nonlinear dynamical systems, and study numerical methods to analyze short as well as long-term responses. Dynamical systems characterized by a system of second-order nonlinear ordinary differential equations (ODEs) are recast into a system of nonlinear first order ODEs in mixed variables of positions as well as velocities. For each discrete-time interval Radial Basis Functions (RBFs) are assumed as trial functions for the mixed variables in the time domain. A simple collocation method is developed in the time-domain, with Legendre-Gauss-Lobatto nodes as RBF source points as well as collocation points.… More >