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  • Open Access

    PROCEEDINGS

    Analysis of High-Order Partial Differential Equations by Using the Generalized Finite Difference Method

    Tsung-Han Li1,*, Chia-Ming Fan1, Po-Wei Li2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.32, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012120

    Abstract The generalized finite difference method (GFDM), which cooperated with the fictitious-nodes technique, is proposed in this study to accurately analyze three-dimensional boundary value problems, governed by high-order partial differential equations. Some physical applications can be mathematically described by boundary value problems governed by high-order partial differential equations, but it is non-trivial to analyze the high-order partial differential equations by adopting conventional mesh-based numerical schemes, such as finite difference method, the finite element method, etc. In this study, the GFDM, a localized meshless method, is proposed to accurately and efficiently solve boundary value problems governed by… More >

  • Open Access

    ARTICLE

    Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

    Meng Ma1,2,*, Liu Fu1,2, Xu Guo3, Zhi Zhai1,2

    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 >

  • Open Access

    ARTICLE

    A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential Equation Model for HIV/AIDS with Treatment Compartment

    Gamze Yıldırım1,2, Şuayip Yüzbaşı3,*

    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 >

  • Open Access

    ARTICLE

    Pervasive Attentive Neural Network for Intelligent Image Classification Based on N-CDE’s

    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 >

  • Open Access

    ARTICLE

    Research on Carbon Emission for Preventive Maintenance of Wind Turbine Gearbox Based on Stochastic Differential Equation

    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

    Research on Carbon Emission for Preventive Maintenance of Wind Turbine Gearbox Based on Stochastic Differential Equation

  • Open Access

    ARTICLE

    Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

    Saima Rashid1,2,*, Fahd Jarad3,4

    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 >

  • Open Access

    ARTICLE

    A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

    Sergiy Reutskiy1, Yuhui Zhang2,*, Jun Lu3,*, 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 >

  • Open Access

    ARTICLE

    Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

    Rania Saadah1, Mohammed Amleh1, Ahmad Qazza1, Shrideh Al-Omari2,*, 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 >

  • Open Access

    ARTICLE

    A Time-Varying Parameter Estimation Method for Physiological Models Based on Physical Information Neural Networks

    Jiepeng Yao1,2, Zhanjia Peng1,2, Jingjing Liu1,2, Chengxiao Fan1,2, Zhongyi Wang1,2,3, Lan Huang1,2,*

    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 >

  • Open Access

    ARTICLE

    Dynamical Analysis of the Stochastic COVID-19 Model Using Piecewise Differential Equation Technique

    Yu-Ming Chu1, Sobia Sultana2, Saima Rashid3,*, 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 >

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