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  • Open Access


    Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

    Nasser Sweilam1, Seham Al-Mekhlafi2,*, Aya Ahmed3, Ahoud Alsheri4, Emad Abo-Eldahab3

    CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1619-1645, 2024, DOI:10.32604/cmes.2024.047896

    Abstract In this paper, two crossover hybrid variable-order derivatives of the cancer model are developed. Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators. The existence, uniqueness, and stability of the proposed model are discussed. Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models. Comparative studies with generalized fifth-order Runge-Kutta method are given. Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented. We have showcased the efficiency of the proposed More >

  • Open Access


    An Effective Runge-Kutta Optimizer Based on Adaptive Population Size and Search Step Size

    Ala Kana, Imtiaz Ahmad*

    CMC-Computers, Materials & Continua, Vol.76, No.3, pp. 3443-3464, 2023, DOI:10.32604/cmc.2023.040775

    Abstract A newly proposed competent population-based optimization algorithm called RUN, which uses the principle of slope variations calculated by applying the Runge Kutta method as the key search mechanism, has gained wider interest in solving optimization problems. However, in high-dimensional problems, the search capabilities, convergence speed, and runtime of RUN deteriorate. This work aims at filling this gap by proposing an improved variant of the RUN algorithm called the Adaptive-RUN. Population size plays a vital role in both runtime efficiency and optimization effectiveness of metaheuristic algorithms. Unlike the original RUN where population size is fixed throughout… More >

  • Open Access



    P.S.S. Nagalakshm*, N. Vijaya

    Frontiers in Heat and Mass Transfer, Vol.14, pp. 1-9, 2020, DOI:10.5098/hmt.14.4

    Abstract In the present investigation is to magnetohydrodymaics (MHD) radiative flow of an incompressible steady flow of Carreau nanofluid explored with carbon nanotubes. The boundary layer flow and heat transfer to a Carreau nanofluid model over a non- linear stretching surface is introduced. The Carreau model, adequate for many non-Newtonian fluids is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical values of the power law exponent n. The modeled boundary layer conservation equations are converted to non-linear coupled ordinary differential equations by a suitable… More >

  • Open Access


    Numerical Computational Heuristic Through Morlet Wavelet Neural Network for Solving the Dynamics of Nonlinear SITR COVID-19

    Zulqurnain Sabir1, Abeer S. Alnahdi2,*, Mdi Begum Jeelani2, Mohamed A. Abdelkawy2,3,*, Muhammad Asif Zahoor Raja4, Dumitru Baleanu5,6, Muhammad Mubashar Hussain7

    CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.2, pp. 763-785, 2022, DOI:10.32604/cmes.2022.018496

    Abstract The present investigations are associated with designing Morlet wavelet neural network (MWNN) for solving a class of susceptible, infected, treatment and recovered (SITR) fractal systems of COVID-19 propagation and control. The structure of an error function is accessible using the SITR differential form and its initial conditions. The optimization is performed using the MWNN together with the global as well as local search heuristics of genetic algorithm (GA) and active-set algorithm (ASA), i.e., MWNN-GA-ASA. The detail of each class of the SITR nonlinear COVID-19 system is also discussed. The obtained outcomes of the SITR system are More >

  • Open Access


    Numerical Analysis of Laterally Loaded Long Piles in Cohesionless Soil

    Ayman Abd-Elhamed1,2,*, Mohamed Fathy3, Khaled M. Abdelgaber1

    CMC-Computers, Materials & Continua, Vol.71, No.2, pp. 2175-2190, 2022, DOI:10.32604/cmc.2022.021899

    Abstract The capability of piles to withstand horizontal loads is a major design issue. The current research work aims to investigate numerically the responses of laterally loaded piles at working load employing the concept of a beam-on-Winkler-foundation model. The governing differential equation for a laterally loaded pile on elastic subgrade is derived. Based on Legendre-Galerkin method and Runge-Kutta formulas of order four and five, the flexural equation of long piles embedded in homogeneous sandy soils with modulus of subgrade reaction linearly variable with depth is solved for both free- and fixed-headed piles. Mathematica, as one of More >

  • Open Access


    IRKO: An Improved Runge-Kutta Optimization Algorithm for Global Optimization Problems

    R. Manjula Devi1, M. Premkumar2, Pradeep Jangir3, Mohamed Abdelghany Elkotb4,5, Rajvikram Madurai Elavarasan6, Kottakkaran Sooppy Nisar7,*

    CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 4803-4827, 2022, DOI:10.32604/cmc.2022.020847

    Abstract Optimization is a key technique for maximizing or minimizing functions and achieving optimal cost, gains, energy, mass, and so on. In order to solve optimization problems, metaheuristic algorithms are essential. Most of these techniques are influenced by collective knowledge and natural foraging. There is no such thing as the best or worst algorithm; instead, there are more effective algorithms for certain problems. Therefore, in this paper, a new improved variant of a recently proposed metaphorless Runge-Kutta Optimization (RKO) algorithm, called Improved Runge-Kutta Optimization (IRKO) algorithm, is suggested for solving optimization problems. The IRKO is formulated… More >

  • Open Access


    New Fuzzy Fractional Epidemic Model Involving Death Population

    Prasantha Bharathi Dhandapani1, Dumitru Baleanu2,3,4,*, Jayakumar Thippan1, Vinoth Sivakumar1

    Computer Systems Science and Engineering, Vol.37, No.3, pp. 331-346, 2021, DOI:10.32604/csse.2021.015619

    Abstract In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) include the death rate as one of the parameters to estimate the change in susceptible, infected and recovered populations. Actually, because of the deficiencies in immunity, even the ordinary flu could cause death. If people’s disease resistance is strong, then serious diseases may not result in mortalities. The classical model always assumes a closed system where there is no new birth… More >

  • Open Access


    NURBS Modeling and Curve Interpolation Optimization of 3D Graphics

    Hao Zhu1,*, Mulan Wang2, Kun Liu2, Weiye Xu3

    CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1799-1811, 2021, DOI:10.32604/cmc.2020.012706

    Abstract In order to solve the problem of complicated Non-Uniform Rational B-Splines (NURBS) modeling and improve the real-time performance of the high-order derivative of the curve interpolation process, the method of NURBS modeling based on the slicing and layering of triangular mesh is introduced. The research and design of NURBS curve interpolation are carried out from the two aspects of software algorithm and hardware structure. Based on the analysis of the characteristics of traditional computing methods with Taylor series expansion, the Adams formula and the Runge-Kutta formula are used in the NURBS curve interpolation process, and More >

  • Open Access


    Residual Correction Procedure with Bernstein Polynomials for Solving Important Systems of Ordinary Differential Equations

    M. H. T. Alshbool1, W. Shatanawi2, 3, 4, *, I. Hashim5, M. Sarr1

    CMC-Computers, Materials & Continua, Vol.64, No.1, pp. 63-80, 2020, DOI:10.32604/cmc.2020.09431

    Abstract One of the most attractive subjects in applied sciences is to obtain exact or approximate solutions for different types of linear and nonlinear systems. Systems of ordinary differential equations like systems of second-order boundary value problems (BVPs), Brusselator system and stiff system are significant in science and engineering. One of the most challenge problems in applied science is to construct methods to approximate solutions of such systems of differential equations which pose great challenges for numerical simulations. Bernstein polynomials method with residual correction procedure is used to treat those challenges. The aim of this paper… More >

  • Open Access


    A Reliable Stochastic Numerical Analysis for Typhoid Fever Incorporating With Protection Against Infection

    Muhammad Shoaib Arif1,*, Ali Raza1, Muhammad Rafiq2, Mairaj Bibi3, Rabia Fayyaz3, Mehvish Naz3, Umer Javed4

    CMC-Computers, Materials & Continua, Vol.59, No.3, pp. 787-804, 2019, DOI:10.32604/cmc.2019.04655

    Abstract In this paper, a reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection has been considered. We have compared the solutions of stochastic and deterministic typhoid fever model. It has been shown that the stochastic typhoid fever model is more realistic as compared to the deterministic typhoid fever model. The effect of threshold number T* hold in stochastic typhoid fever model. The proposed framework of the stochastic non-standard finite difference scheme (SNSFD) preserves all dynamical properties like positivity, bounded-ness and dynamical consistency defined by Mickens, R. E. The stochastic numerical simulation of More >

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