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  • Open Access


    Three-Dimensional Numerical Simulation of Large-Scale LandslideGenerated Surging Waves with a GPU‒Accelerated Soil‒Water Coupled SPH Model

    Can Huang1,*, Xiaoliang Wang1, Qingquan Liu1, Huaning Wang2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.25, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09824

    Abstract Soil‒water coupling is an important process in landslide-generated impulse waves (LGIW) problems, accompanied by large deformation of soil, strong interface coupling and three-dimensional effect. A meshless particle method, smooth particle hydrodynamics (SPH) has great advantages in dealing with complex interface and multiphase coupling problems. This study presents an improved soil‒water coupled model to simulate LGIW problems based on an open source code DualSPHysics (v4.0). Aiming to solve the low efficiency problem in modeling real large-scale LGIW problems, graphics processing unit (GPU) acceleration technology is implemented into this code. An experimental example, subaerial landslidegenerated water waves, is simulated to validate this… More >

  • Open Access


    Computational Approximations for Real-World Application of Epidemic Model

    Shami A. M. Alsallami1, Ali Raza2,*, Mona Elmahi3, Muhammad Rafiq4, Shamas Bilal5, Nauman Ahmed6, Emad E. Mahmoud7

    Intelligent Automation & Soft Computing, Vol.33, No.3, pp. 1923-1939, 2022, DOI:10.32604/iasc.2022.024993

    Abstract The real-world applications and analysis have a significant role in the scientific literature. For instance, mathematical modeling, computer graphics, camera, operating system, Java, disk encryption, web, streaming, and many more are the applications of real-world problems. In this case, we consider disease modeling and its computational treatment. Computational approximations have a significant role in different sciences such as behavioral, social, physical, and biological sciences. But the well-known techniques that are widely used in the literature have many problems. These methods are not consistent with the physical nature and even violate the actual behavior of the continuous model. The structural properties… 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


    Analysis of Pneumonia Model via Efficient Computing Techniques

    Kamaledin Abodayeh1, Ali Raza2,3,*, Muhammad Rafiq4, Muhammad Shoaib Arif5, Muhammad Naveed5, Zunir Zeb3, Syed Zaheer Abbas3, Kiran Shahzadi3, Sana Sarwar3, Qasim Naveed3, Badar Ul Zaman3, Muhammad Mohsin6

    CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 6073-6088, 2022, DOI:10.32604/cmc.2022.020732

    Abstract Pneumonia is a highly transmissible disease in children. According to the World Health Organization (WHO), the most affected regions include south Asia and sub-Saharan Africa. Worldwide, 15% of pediatric deaths can be attributed to pneumonia. Computing techniques have a significant role in science, engineering, and many other fields. In this study, we focused on the efficiency of numerical techniques via computer programs. We studied the dynamics of the pneumonia-like infections of epidemic models using numerical techniques. We discuss two types of analysis: dynamical and numerical. The dynamical analysis included positivity, boundedness, local stability, reproduction number, and equilibria of the model.… More >

  • Open Access


    Design of Computer Methods for the Solution of Cervical Cancer Epidemic Model

    Ali Raza1, Muhammad Rafiq2, Dalal Alrowaili3, Nauman Ahmed4, Ilyas Khan5,*, Kottakkaran Sooppy Nisar6, Muhammad Mohsin7

    CMC-Computers, Materials & Continua, Vol.70, No.1, pp. 1649-1666, 2022, DOI:10.32604/cmc.2022.019148

    Abstract Nonlinear modelling has a significant role in different disciplines of sciences such as behavioral, social, physical and biological sciences. The structural properties are also needed for such types of disciplines, as dynamical consistency, positivity and boundedness are the major requirements of the models in these fields. One more thing, this type of nonlinear model has no explicit solutions. For the sake of comparison its computation will be done by using different computational techniques. Regrettably, the aforementioned structural properties have not been restored in the existing computational techniques in literature. Therefore, the construction of structural preserving computational techniques are needed. The… More >

  • Open Access


    A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

    I. G. Ameen1, N. A. Elkot2, M. A. Zaky3,*, A. S. Hendy4,5, E. H. Doha2

    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 21-41, 2021, DOI:10.32604/cmes.2021.015310

    Abstract We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left- and right-sided fractional derivatives. The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations. Then, a Legendre-based spectral collocation method is developed for solving the transformed system. Therefore, we can make good use of the advantages of the Gauss quadrature rule. We present the construction and analysis of the collocation method. These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange equations. Two numerical examples… More >

  • Open Access


    Spectral Solutions of Linear and Nonlinear BVPs Using Certain Jacobi Polynomials Generalizing Third- and Fourth-Kinds of Chebyshev Polynomials

    W. M. Abd-Elhameed1,2,*, Asmaa M. Alkenedri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 955-989, 2021, DOI:10.32604/cmes.2021.013603

    Abstract This paper is dedicated to implementing and presenting numerical algorithms for solving some linear and nonlinear even-order two-point boundary value problems. For this purpose, we establish new explicit formulas for the high-order derivatives of certain two classes of Jacobi polynomials in terms of their corresponding Jacobi polynomials. These two classes generalize the two celebrated non-symmetric classes of polynomials, namely, Chebyshev polynomials of third- and fourth-kinds. The idea of the derivation of such formulas is essentially based on making use of the power series representations and inversion formulas of these classes of polynomials. The derived formulas serve in converting the even-order… More >

  • Open Access


    An Effective Numerical Method for the Solution of a Stochastic Coronavirus (2019-nCovid) Pandemic Model

    Wasfi Shatanawi1,2,3, Ali Raza4,5,*, Muhammad Shoaib Arif4, Kamaledin Abodayeh1, Muhammad Rafiq6, Mairaj Bibi7

    CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1121-1137, 2021, DOI:10.32604/cmc.2020.012070

    Abstract Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic… More >

  • Open Access


    A Numerical Efficient Technique for the Solution of Susceptible Infected Recovered Epidemic Model

    Muhammad Shoaib Arif1,*, Ali Raza1,2, Kamaleldin Abodayeh3, Muhammad Rafiq4, Mairaj Bibi5, Amna Nazeer5

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 477-491, 2020, DOI:10.32604/cmes.2020.011121

    Abstract The essential features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. The aim of our paper, to achieve the comparison analysis of the stochastic susceptible, infected recovered epidemic model. The stochastic modelling is a realistic way to study the dynamics of compartmental modelling as compared to deterministic modelling. The effect of reproduction number has also observed in the stochastic susceptible, infected recovered epidemic model. For comparison analysis, we developed some explicit stochastic techniques, but they are the time-dependent techniques. The implicitly driven… More >

  • Open Access


    Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate

    Wasfi Shatanawi1, 2, 3, Muhammad Shoaib Arif4, *, Ali Raza4, Muhammad Rafiq5, Mairaj Bibi6, Javeria Nawaz Abbasi6

    CMC-Computers, Materials & Continua, Vol.64, No.2, pp. 797-811, 2020, DOI:10.32604/cmc.2020.010759

    Abstract The structure-preserving features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. Unfortunately, the existing stochastic approaches in literature do not restore aforesaid structure-preserving features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the structure-preserving features preserving numerical approach. This writing aims to describe the structure-preserving dynamics of the stochastic model. We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling. The usual explicit… More >

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