Meng Ma^1,2,*, Liu Fu^1,2, Xu Guo³, Zhi Zhai^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 385-399, 2024, DOI:10.32604/cmes.2024.052585 - 20 August 2024

Abstract Partial Differential Equation (PDE) is among the most fundamental tools employed to model dynamic systems. Existing PDE modeling methods are typically derived from established knowledge and known phenomena, which are time-consuming and labor-intensive. Recently, discovering governing PDEs from collected actual data via Physics Informed Neural Networks (PINNs) provides a more efficient way to analyze fresh dynamic systems and establish PED models. This study proposes Sequentially Threshold Least Squares-Lasso (STLasso), a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares (STLS) algorithm, which can complete sparse regression of PDE coefficients with the constraints More >

Gamze Yıldırım^1,2, Şuayip Yüzbaşı^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 281-310, 2024, DOI:10.32604/cmes.2024.052181 - 20 August 2024

Abstract In this study, a numerical method based on the Pell-Lucas polynomials (PLPs) is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment. The HIV/AIDS mathematical model with a treatment compartment is divided into five classes, namely, susceptible patients (S), HIV-positive individuals (I), individuals with full-blown AIDS but not receiving ARV treatment (A), individuals being treated (T), and individuals who have changed their sexual habits sufficiently (R). According to the method, by utilizing the PLPs and the collocation points, we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into… More >

Anas W. Abulfaraj^*

CMC-Computers, Materials & Continua, Vol.79, No.1, pp. 1137-1156, 2024, DOI:10.32604/cmc.2024.047945 - 25 April 2024

Abstract The utilization of visual attention enhances the performance of image classification tasks. Previous attention-based models have demonstrated notable performance, but many of these models exhibit reduced accuracy when confronted with inter-class and intra-class similarities and differences. Neural-Controlled Differential Equations (N-CDE’s) and Neural Ordinary Differential Equations (NODE’s) are extensively utilized within this context. N-CDE’s possesses the capacity to effectively illustrate both inter-class and intra-class similarities and differences with enhanced clarity. To this end, an attentive neural network has been proposed to generate attention maps, which uses two different types of N-CDE’s, one for adopting hidden layers… More >

Hongsheng Su, Lixia Dong^*, Xiaoying Yu, Kai Liu

Energy Engineering, Vol.121, No.4, pp. 973-986, 2024, DOI:10.32604/ee.2023.043497 - 26 March 2024

Abstract Time based maintenance (TBM) and condition based maintenance (CBM) are widely applied in many large wind farms to optimize the maintenance issues of wind turbine gearboxes, however, these maintenance strategies do not take into account environmental benefits during full life cycle such as carbon emissions issues. Hence, this article proposes a carbon emissions computing model for preventive maintenance activities of wind turbine gearboxes to solve the issue. Based on the change of the gearbox state during operation and the influence of external random factors on the gearbox state, a stochastic differential equation model (SDE) and More > Graphic Abstract

Saima Rashid^1,2,*, Fahd Jarad^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2289-2327, 2024, DOI:10.32604/cmes.2023.028773 - 11 March 2024

Abstract Because of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic More >

Sergiy Reutskiy¹, Yuhui Zhang^2,*, Jun Lu^3,*, Ciren Pubu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1583-1612, 2024, DOI:10.32604/cmes.2023.044878 - 29 January 2024

Abstract This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations (FODEs) which have been widely used in modeling various phenomena in engineering and science. An approximate solution of the system is sought in the form of the finite series over the Müntz polynomials. By using the collocation procedure in the time interval, one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure. This technique also serves as the basis for solving the time-fractional partial differential equations More >

Rania Saadah¹, Mohammed Amleh¹, Ahmad Qazza¹, Shrideh Al-Omari^2,*, Ahmet Ocak Akdemir³

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1593-1616, 2024, DOI:10.32604/cmes.2023.029180 - 17 November 2023

Abstract In this study, we aim to investigate certain triple integral transform and its application to a class of partial differential equations. We discuss various properties of the new transform including inversion, linearity, existence, scaling and shifting, etc. Then, we derive several results enfolding partial derivatives and establish a multi-convolution theorem. Further, we apply the aforementioned transform to some classical functions and many types of partial differential equations involving heat equations, wave equations, Laplace equations, and Poisson equations as well. Moreover, we draw some figures to illustrate 3-D contour plots for exact solutions of some selected More >

Jiepeng Yao^1,2, Zhanjia Peng^1,2, Jingjing Liu^1,2, Chengxiao Fan^1,2, Zhongyi Wang^1,2,3, Lan Huang^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2243-2265, 2023, DOI:10.32604/cmes.2023.028101 - 03 August 2023

Abstract In the establishment of differential equations, the determination of time-varying parameters is a difficult problem, especially for equations related to life activities. Thus, we propose a new framework named BioE-PINN based on a physical information neural network that successfully obtains the time-varying parameters of differential equations. In the proposed framework, the learnable factors and scale parameters are used to implement adaptive activation functions, and hard constraints and loss function weights are skillfully added to the neural network output to speed up the training convergence and improve the accuracy of physical information neural networks. In this… More >

Yu-Ming Chu¹, Sobia Sultana², Saima Rashid^3,*, Mohammed Shaaf Alharthi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2427-2464, 2023, DOI:10.32604/cmes.2023.028771 - 03 August 2023

Abstract Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous. Two examples are the spread of Spanish flu and COVID-19. The aim of this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators. Firstly, the strength number of the deterministic case is carried out. Then, for the stochastic model, we show that there is a critical number that can predict virus persistence and infection eradication. Because of the peculiarity of More >

V.S. Sampath Kumar, N.P. Pai^† , B. Devaki

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-13, 2023, DOI:10.5098/hmt.20.30

Abstract In the present study, we consider Casson fluid flow between two porous plates with permeability criteria in the presence of heat transfer and magnetic effect. A proper set of similarity transformations simplify the Navier-Stokes equations to non-linear ODEs with boundary conditions. The homotopy perturbation method is an efficient and stable method which is used to get solutions. Further, the results obtained are compared with the solution computed through an effective and efficient finite difference approach. The purpose of this analysis is to study the four different cases arise viz: suction, injection, mixed suction and mixed More >