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  • Open Access


    A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations

    Dumitru Baleanu1,2,3, Mehran Namjoo4, Ali Mohebbian4, Amin Jajarmi5,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1147-1163, 2023, DOI:10.32604/cmes.2022.022403

    Abstract In the present paper, the numerical solution of Itô type stochastic parabolic equation with a time white noise process is imparted based on a stochastic finite difference scheme. At the beginning, an implicit stochastic finite difference scheme is presented for this equation. Some mathematical analyses of the scheme are then discussed. Lastly, to ascertain the efficacy and accuracy of the suggested technique, the numerical results are discussed and compared with the exact solution. More >

  • Open Access


    Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

    Lei Wang1,2,*, Yuxin Qi1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 325-339, 2023, DOI:10.32604/cmes.2022.019730

    Abstract Currently, energy conservation draws wide attention in industrial manufacturing systems. In recent years, many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach. This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects. In it, the real processing time of jobs is calculated by using their processing speed and normal processing time. To describe this problem in a mathematical way, a multi-objective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated. More >

  • Open Access


    Estimating Fuel-Efficient Air Plane Trajectories Using Machine Learning

    Jaiteg Singh1, Gaurav Goyal1, Farman Ali2, Babar Shah3, Sangheon Pack4,*

    CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 6189-6204, 2022, DOI:10.32604/cmc.2022.021657

    Abstract Airline industry has witnessed a tremendous growth in the recent past. Percentage of people choosing air travel as first choice to commute is continuously increasing. Highly demanding and congested air routes are resulting in inadvertent delays, additional fuel consumption and high emission of greenhouse gases. Trajectory planning involves creation identification of cost-effective flight plans for optimal utilization of fuel and time. This situation warrants the need of an intelligent system for dynamic planning of optimized flight trajectories with least human intervention required. In this paper, an algorithm for dynamic planning of optimized flight trajectories has… More >

  • Open Access


    Numerical Simulations for Stochastic Computer Virus Propagation Model

    Muhammad Shoaib Arif1, *, Ali Raza1, Muhammad Rafiq2, Mairaj Bibi3, Javeria Nawaz Abbasi3, Amna Nazeer3, Umer Javed4

    CMC-Computers, Materials & Continua, Vol.62, No.1, pp. 61-77, 2020, DOI:10.32604/cmc.2020.08595

    Abstract We are presenting the numerical simulations for the stochastic computer virus propagation model in this manuscript. We are comparing the solutions of stochastic and deterministic computer virus models. Outcomes of a threshold number R0 hold in stochastic computer virus model. If R0 < 1 then in such a condition virus controlled in the computer population while R0 > 1 shows virus rapidly spread in the computer population. Unfortunately, stochastic numerical techniques fail to cope with large step sizes of time. The suggested structure of the stochastic non-standard finite difference technique can never violate the dynamical properties. On More >

  • Open Access


    A Stochastic Analysis of a Brownian Ratchet Model for Actin-Based Motility

    Hong Qian1

    Molecular & Cellular Biomechanics, Vol.1, No.4, pp. 267-278, 2004, DOI:10.3970/mcb.2004.001.267

    Abstract In recent single-particle tracking (SPT) measurements on Listeria monocytogenes motility in cells [Kuo and McGrath (2000)], the actin-based stochastic dynamics of the bacterium movement has been analyzed statistically in terms of the mean-square displacement (MSD) of the trajectory. We present a stochastic analysis of a simplified polymerization Brownian ratchet (BR) model in which motions are limited by the bacterium movement. Analytical results are obtained and statistical data analyses are investigated. It is shown that the MSD of the stochastic bacterium movement is a monotonic quadratic function while the MSD for detrended trajectories is linear. Both the More >

  • Open Access


    Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

    C. R. A. Silva1, H. P. Azikri de Deus1, G.E. Mantovani2, A.T. Beck3

    CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.2, pp. 119-150, 2010, DOI:10.3970/cmes.2010.067.119

    Abstract In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value More >

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