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  • Open Access


    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

    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 (PDEs). The modified radial basis… More >

  • Open Access


    Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

    David Tae, Kumar K. Tamma*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 843-885, 2023, DOI:10.32604/cmes.2023.023071

    Abstract We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method, particle methods, and other spatial methods on a single body sub-divided into multiple subdomains. This is in conjunction with implementing the well known Generalized Single Step Single Solve (GS4) family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework. In the current state of technology, the coupling of altogether different… More >

  • Open Access


    Reducing the Range of Cancer Risk on BI-RADS 4 Subcategories via Mathematical Modelling

    Nezihal Gokbulut1,2, Evren Hincal1,2,*, Hasan Besim3, Bilgen Kaymakamzade1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 93-109, 2022, DOI:10.32604/cmes.2022.019782

    Abstract Breast Imaging Reporting and Data System, also known as BI-RADS is a universal system used by radiologists and doctors. It constructs a comprehensive language for the diagnosis of breast cancer. BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories. Mathematical models play an important role in the diagnosis and treatment of cancer. In this study, data of 42 BI-RADS 4 patients taken from the Center for Breast Health, Near East University Hospital is utilized. Regarding the analysis, a mathematical model is constructed by dividing the population into 4 compartments. Sensitivity analysis is… More >

  • Open Access


    Navier Slip and Heat Transfer in a Nanofluid Due to a Stretching/Shrinking Sheet: An Analytical Study

    A. B. Vishalakshi1, U. S. Mahabaleshwar1,*, M. EL. Ganaoui2, R. Bennacer3

    FDMP-Fluid Dynamics & Materials Processing, Vol.18, No.5, pp. 1551-1567, 2022, DOI:10.32604/fdmp.2022.021949

    Abstract This paper is devoted to the analysis of the heat transfer and Navier’s slip effects in a non-Newtonian Jeffrey fluid flowing past a stretching/shrinking sheet. The nanoparticles, namely, Cu and Al2O3 are used with a water-based fluid with Prandtl number 6.272. Velocity slip flow is assumed to occur when the characteristic size of the flow system is small or the flow pressure is very small. By using the similarity transformations, the governing nonlinear PDEs are turned into ordinary differential equations (ODE’s). Analytical results are presented and analyzed for various values of physical parameters: Prandtl number, Radiation parameter, stretching/shrinking parameter and… More >

  • Open Access


    Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

    Hira Soomro1,*, Nooraini Zainuddin1, Hanita Daud1, Joshua Sunday2

    CMC-Computers, Materials & Continua, Vol.72, No.2, pp. 2947-2961, 2022, DOI:10.32604/cmc.2022.025933

    Abstract Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost. The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency. Hybrid block methods for instance are specifically used in numerical integration of initial value problems. In this paper, an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations (ODEs). In deriving the method, the Lagrange interpolation polynomial was employed based on some data points… More >

  • Open Access


    An Alternative Algorithm for the Symmetry Classification of Ordinary Differential Equations

    Yi Tian1,2,*, Jing Pang3,4

    Sound & Vibration, Vol.56, No.1, pp. 65-76, 2022, DOI:10.32604/sv.2022.014547

    Abstract This is the first paper on symmetry classification for ordinary differential equations (ODEs) based on Wu’s method. We carry out symmetry classification of two ODEs, named the generalizations of the Kummer-Schwarz equations which involving arbitrary function. First, Lie algorithm is used to give the determining equations of symmetry for the given equations, which involving arbitrary functions. Next, differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets, which are easy to be solved relatively. Each branch of the decomposition yields a class of symmetries and associated parameters.… More >

  • Open Access


    Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19

    Zafar Iqbal1,2, Muhammad Aziz-ur Rehman1, Nauman Ahmed1,2, Ali Raza3,4, Muhammad Rafiq5, Ilyas Khan6,*, Kottakkaran Sooppy Nisar7

    CMC-Computers, Materials & Continua, Vol.71, No.2, pp. 2141-2157, 2022, DOI:10.32604/cmc.2022.013906

    Abstract In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on… More >

  • Open Access


    Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some Error Analysis

    Radwan Abu-Gdairi1, Shatha Hasan2, Shrideh Al-Omari3,*, Mohammad Al-Smadi2,4, Shaher Momani4,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 299-313, 2022, DOI:10.32604/cmes.2022.017010

    Abstract In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform form for a rapidly convergent series in the posed Sobolev space. Using the Gram-Schmidt orthogonality process, complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction. Consequently, by applying the standard RKHS method to each subinterval, approximate solutions that converge uniformly to the exact solutions are obtained. For this purpose,… More >

  • Open Access


    An Uncertainty Analysis Method for Artillery Dynamics with Hybrid Stochastic and Interval Parameters

    Liqun Wang1, Zengtao Chen2, Guolai Yang1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 479-503, 2021, DOI:10.32604/cmes.2021.011954

    Abstract This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion (PCE). The uncertainty parameters with sufficient information are regarded as stochastic variables, whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge. In this method, the PCE model is constructed through the Galerkin projection method, in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights. Through the sampling in PCE, the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems, without changing… More >

  • Open Access


    Essential Features Preserving Dynamics of Stochastic Dengue Model

    Wasfi Shatanawi1,2,3, Ali Raza4,5,*, Muhammad Shoaib Arif4, Muhammad Rafiq6, Mairaj Bibi7, Muhammad Mohsin8

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 201-215, 2021, DOI:10.32604/cmes.2021.012111

    Abstract Nonlinear stochastic modelling plays an important character in the different fields of sciences such as environmental, material, engineering, chemistry, physics, biomedical engineering, and many more. In the current study, we studied the computational dynamics of the stochastic dengue model with the real material of the model. Positivity, boundedness, and dynamical consistency are essential features of stochastic modelling. Our focus is to design the computational method which preserves essential features of the model. The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature. Analysis and comparison were explored in favour of convergence. Also, we… More >

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