Mairaj Bibi¹, Muhammad Shoaib Arif ², Yasir Nawaz³, Nabil Kerdid^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.1, pp. 537-569, 2025, DOI:10.32604/cmes.2025.070362 - 30 October 2025

Abstract This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity, thermal radiation, and coupled heat and mass transfer effects. A modified two-stage Exponential Time Integrator is introduced for temporal discretization, providing second-order accuracy in time. A compact finite difference method is employed for spatial discretization, yielding sixth-order accuracy at most grid points. The proposed framework ensures numerical stability and convergence when solving stiff, nonlinear parabolic systems arising in fluid flow and heat transfer problems. The novelty of the work lies in combining exponential integrator schemes with compact… 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 >

Jialun Lin¹, Qiong Chen^1,2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1549-1561, 2024, DOI:10.32604/cmes.2023.029631 - 17 November 2023

Abstract Watermarks can provide reliable and secure copyright protection for optical coherence tomography (OCT) fundus images. The effective image segmentation is helpful for promoting OCT image watermarking. However, OCT images have a large amount of low-quality data, which seriously affects the performance of segmentation methods. Therefore, this paper proposes an effective segmentation method for OCT fundus image watermarking using a rough convolutional neural network (RCNN). First, the rough-set-based feature discretization module is designed to preprocess the input data. Second, a dual attention mechanism for feature channels and spatial regions in the CNN is added to enable… More >

Zi Han^1,*, Zhentian Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 245-272, 2024, DOI:10.32604/cmes.2023.029708 - 22 September 2023

Abstract In the context of global mean square error concerning the number of random variables in the representation, the Karhunen–Loève (KL) expansion is the optimal series expansion method for random field discretization. The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem (IEVP). The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares (MLS), least squares (LS), and finite element method (FEM) to solve the IEVP. Compared with the Galerkin method based on finite element or Legendre polynomials,… More > Graphic Abstract

Andang Sunarto^1,*, Praveen Agarwal^2,3,4, Jumat Sulaiman⁵, Jackel Vui Lung Chew⁶

Intelligent Automation & Soft Computing, Vol.31, No.2, pp. 1173-1184, 2022, DOI:10.32604/iasc.2022.020542 - 22 September 2021

Abstract Solving time-fractional diffusion equation using a numerical method has become a research trend nowadays since analytical approaches are quite limited. There is increasing usage of the finite difference method, but the efficiency of the scheme still needs to be explored. A half-sweep finite difference scheme is well-known as a computational complexity reduction approach. Therefore, the present paper applied an unconditionally stable half-sweep finite difference scheme to solve the time-fractional diffusion equation in a one-dimensional model. Throughout this paper, a Caputo fractional operator is used to substitute the time-fractional derivative term approximately. Then, the stability of… More >

Nauman Ahmed^1,2, Umbreen Fatima¹, Shahzaib Iqbal¹, Ali Raza³, Muhammad Rafiq^4,*, Muhammad Aziz-ur-Rehman², Shehla Saeed¹, Ilyas Khan⁵, Kottakkaran Sooppy Nisar⁶

CMC-Computers, Materials & Continua, Vol.68, No.1, pp. 201-212, 2021, DOI:10.32604/cmc.2021.014171 - 22 March 2021

Abstract The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered (SLBR) epidemic model. It describes the computer virus dynamics with vertical transmission via the internet. In these types of dynamics models, the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design. By taking into account this key property, the positivity preserving algorithm is designed to solve the underlying SLBR system. Since, the state variables associated with the phenomenon, represent the computer nodes, so they must take in absolute. Moreover, the continuous system More >

Rafael Company¹, Vera N. Egorova², Lucas Jódar^1,*, Ferran Fuster Valls³

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 493-508, 2020, DOI:10.32604/cmes.2020.010208 - 20 July 2020

Abstract A numerical method for American options pricing on assets under the Heston stochastic volatility model is developed. A preliminary transformation is applied to remove the mixed derivative term avoiding known numerical drawbacks and reducing computational costs. Free boundary is treated by the penalty method. Transformed nonlinear partial differential equation is solved numerically by using the method of lines. For full discretization the exponential time differencing method is used. Numerical analysis establishes the stability and positivity of the proposed method. The numerical convergence behaviour and effectiveness are investigated in extensive numerical experiments. More >

Yongwei Wang¹, Fei Han^2,*, Gilles Lubineau^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.2, pp. 399-423, 2019, DOI:10.32604/cmes.2019.07192

Abstract Classical continuum mechanics which leads to a local continuum model, encounters challenges when the discontinuity appears, while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost. A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages. This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials. Then this hybrid local/nonlocal continuum model is applied to fracture simulation. Some numerical examples like a plate with a hole, Brazilian disk, notched plate and More >

Darin Koblick^1,2,3, Shujing Xu⁴, Joshua Fogel⁵, Praveen Shankar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 1-27, 2016, DOI:10.3970/cmes.2016.111.001

Abstract The Modified Picard-Chebyshev Method (MPCM) is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints. The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine, SNOPT with numerical force models for both Two-Body and J2 perturbations. It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers, such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods. More >

Weiwei Zhang¹, Yufeng Nie¹, Li Cai¹, Nan Qi²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.1, pp. 55-82, 2014, DOI:10.3970/cmes.2014.102.055

Abstract In this paper, we derive an adaptive mesh generation method for discretizing the incompressible flow using node-based local grids. The flow problem is described by the Stokes equations which are solved by a stabilized low-order P1-P1 (linear velocity, linear pressure) mixed finite element method. The proposed node-based adaptive mesh generation method consists of four components: mesh size modification, a node placement procedure, a node-based local mesh generation strategy and an error estimation technique, which are combined so as to guarantee obtaining a conforming refined/coarsened mesh. The nodes are considered as particles with interaction forces, which… More >