Junseo Lee¹, Bongsoo Jang¹, Umer Saeed^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 2165-2189, 2025, DOI:10.32604/cmes.2025.069023 - 31 August 2025

Abstract In recent years, variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability to model complex physical phenomena with memory and spatial heterogeneity. However, existing numerical methods often struggle with the computational challenges posed by such equations, especially in nonlinear, multi-term formulations. This study introduces two hybrid numerical methods—the Linear-Sine and Cosine (L1-CAS) and fast-CAS schemes—for solving linear and nonlinear multi-term Caputo variable-order (CVO) fractional partial differential equations. These methods combine CAS wavelet-based spatial discretization with L1 and fast algorithms in the time domain. A key feature of the approach is More >

Benjamin Wacker¹, Jan Christian Schlüter^2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 2191-2229, 2025, DOI:10.32604/cmes.2025.067397 - 31 August 2025

Abstract In this work, we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution. As our first contribution, we establish non-negativity, boundedness of some solution components, existence globally in time, and uniqueness on a time interval for an arbitrary for the time-continuous problem which extends known results of Kirschner’s model in the literature. As our second analytical result, we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question. Our More >

Pugazhenthi Sivasankar^1,*, Austin B. Probe², Tarek A. Elgohary¹

Digital Engineering and Digital Twin, Vol.2, pp. 169-205, 2024, DOI:10.32604/dedt.2024.052805 - 31 December 2024

Abstract In Space Situational Awareness (SSA), accurate and efficient uncertainty quantification and propagation are essential for various applications, such as conjunction analysis, track correlation, and orbit prediction. The propagation of the probability density function (PDF) in nonlinear systems results in non-Gaussian distributions, which are difficult to approximate. Furthermore, the computational cost of approximating the PDF increases exponentially with the number of random variables, a phenomenon known as the curse of dimensionality. To address these challenges, the Orthogonal Probability Approximation (OPA) method is presented for high-fidelity uncertainty propagation and PDF approximation in nonlinear dynamical systems. The method… More >

Yuxiang Peng^1,*, Pengnan Sun¹, Niannian Liu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.3, pp. 1-1, 2024, DOI:10.32604/icces.2024.011902

Abstract Immersed boundary method (IBM) has been widely applied in the simulation of fluid-structure interaction problems. The traditional direct force model is less accurate, and the sharp-interface approaches involve complex topological operations which are not conducive to dealing with complex structures. The boundary data immersion method (BDIM) is a new fluid-structure coupling scheme that does not need to cut the mesh and can be extended to reach second-order accuracy. However, the traditional boundary data immersion method needs special treatment to deal with the sharp corners of the structure. In the present work, the volume fraction of More >

Sara Salem Alzaid¹, Badr Saad T. Alkahtani^1,*, Kumar Chandan², Ravikumar Shashikala Varun Kumar³

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.3, pp. 2555-2574, 2024, DOI:10.32604/cmes.2024.055312 - 31 October 2024

Abstract Heat transport has been significantly enhanced by the widespread usage of extended surfaces in various engineering domains. Gas turbine blade cooling, refrigeration, and electronic equipment cooling are a few prevalent applications. Thus, the thermal analysis of extended surfaces has been the subject of a significant assessment by researchers. Motivated by this, the present study describes the unsteady thermal dispersal phenomena in a wavy fin with the presence of convection heat transmission. This analysis also emphasizes a novel mathematical model in accordance with transient thermal change in a wavy profiled fin resulting from convection using the… More >

Biao Wang¹, Yuxiang Peng^1,*, Wenhua Xu²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.3, pp. 1-2, 2024, DOI:10.32604/icces.2024.012061

Abstract The damage process of ship structures under near-field underwater explosions involves strong nonlinear coupling effects of multiple media, and its numerical simulation poses a serious challenge to traditional numerical algorithms. Based on previous research, this article first establishes a highly compressible multiphase flow numerical calculation model based on the high-precision Discontinuous Galerkin Method (DGM) and a ship elastic-plastic damage dynamic model based on the meshless Reproducing Kernel Particle Method (RKPM). Furthermore, we develop an algorithm for grid-independent dynamic expansion of cracks. Based on this, the Boundary Data Immersion Method (BDIM) is used to couple the More >

Javaid Ali¹, Armando Ciancio², Kashif Ali Khan³, Nauman Raza^4,5, Haci Mehmet Baskonus^6,*, Muhammad Luqman¹, Zafar-Ullah Khan⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.3, pp. 2275-2296, 2024, DOI:10.32604/cmes.2024.046923 - 08 July 2024

Abstract This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic (CCE) model. The underlying CCE model lacks a closed-form exact solution. Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties, such as positivity, boundedness, and feasibility. Therefore, the development of structure-preserving semi-analytical approaches is always necessary. This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem. Singularity-free safe Padé rational functions approximate the mathematical More >

Ying Qu¹, Jinhao Wang¹, Xueting Cheng¹, Jie Hao¹, Weiru Wang¹, Zhewen Niu², Yuxiang Wu^2,*

Energy Engineering, Vol.121, No.7, pp. 1847-1863, 2024, DOI:10.32604/ee.2024.048300 - 11 June 2024

Abstract The data-driven transient stability assessment (TSA) of power systems can predict online real-time prediction by learning the temporal features before and after faults. However, the accuracy of the assessment is limited by the quality of the data and has weak transferability. Based on this, this paper proposes a method for TSA of power systems based on an improved extreme gradient boosting (XGBoost) model. Firstly, the gradient detection method is employed to remove noise interference while maintaining the original time series trend. On this basis, a focal loss function is introduced to guide the training of… More >

Radwan Abu-Gdairi¹, R. Mareay^2,*, M. Badr³

CMC-Computers, Materials & Continua, Vol.79, No.1, pp. 1025-1038, 2024, DOI:10.32604/cmc.2024.048647 - 25 April 2024

Abstract Recently, much interest has been given to multi-granulation rough sets (MGRS), and various types of MGRS models have been developed from different viewpoints. In this paper, we introduce two techniques for the classification of MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novel approximation space is established by leveraging the underlying topological structure. The characteristics of the newly proposed approximation space are discussed. We introduce an algorithm for the reduction of multi-relations. Secondly, a new approach for the classification of MGRS based on neighborhood concepts is introduced. Finally, a real-life More >

Debiao Meng^1,2,*, Yipeng Guo^1,2, Yihe Xu³, Shiyuan Yang^1,2,*, Yongqiang Guo⁴, Lidong Pan⁴, Xinkai Guo²

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2329-2359, 2024, DOI:10.32604/cmes.2024.047507 - 11 March 2024

Abstract The escalating need for reliability analysis (RA) and reliability-based design optimization (RBDO) within engineering challenges has prompted the advancement of saddlepoint approximation methods (SAM) tailored for such problems. This article offers a detailed overview of the general SAM and summarizes the method characteristics first. Subsequently, recent enhancements in the SAM theoretical framework are assessed. Notably, the mean value first-order saddlepoint approximation (MVFOSA) bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation (MVSOSA); the latter serves as an auxiliary approach to the former. Their distinction is rooted in the varying expansion orders… More >