Home / Advanced Search

  • Title/Keywords

  • Author/Affliations

  • Journal

  • Article Type

  • Start Year

  • End Year

Update SearchingClear
  • Articles
  • Online
Search Results (93)
  • Open Access

    ARTICLE

    Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

    Ahmed M. Elshenhab1,2,*, Xingtao Wang1, Fatemah Mofarreh3, Omar Bazighifan4,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 927-940, 2023, DOI:10.32604/cmes.2022.021512 - 31 August 2022

    Abstract We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayed matrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results. More >

  • Open Access

    ARTICLE

    LaNets: Hybrid Lagrange Neural Networks for Solving Partial Differential Equations

    Ying Li1, Longxiang Xu1, Fangjun Mei1, Shihui Ying2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 657-672, 2023, DOI:10.32604/cmes.2022.021277 - 24 August 2022

    Abstract We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations. That is, we embed Lagrange interpolation and small sample learning into deep neural network frameworks. Concretely, we first perform Lagrange interpolation in front of the deep feedforward neural network. The Lagrange basis function has a neat structure and a strong expression ability, which is suitable to be a preprocessing tool for pre-fitting and feature extraction. Second, we introduce small sample learning into training, which is beneficial to guide the model to be corrected quickly. Taking advantages of More >

  • Open Access

    ARTICLE

    Near Term Hybrid Quantum Computing Solution to the Matrix Riccati Equations

    Augusto González Bonorino1,*, Malick Ndiaye2, Casimer DeCusatis2

    Journal of Quantum Computing, Vol.4, No.3, pp. 135-146, 2022, DOI:10.32604/jqc.2022.036706 - 03 July 2023

    Abstract The well-known Riccati differential equations play a key role in many fields, including problems in protein folding, control and stabilization, stochastic control, and cybersecurity (risk analysis and malware propagation). Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms. While systems with many qubits are still under development, there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations. In this paper, we propose a hybrid quantum-classical algorithm, the Matrix Riccati Solver (MRS). This approach uses a transformation of More >

  • Open Access

    ARTICLE

    An Efficient Computational Method for Differential Equations of Fractional Type

    Mustafa Turkyilmazoglu1,2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 47-65, 2022, DOI:10.32604/cmes.2022.020781 - 18 July 2022

    Abstract An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L2 norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus More >

  • Open Access

    ARTICLE

    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 - 18 July 2022

    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… More >

  • Open Access

    ARTICLE

    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 - 27 May 2022

    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… More >

  • Open Access

    ARTICLE

    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 - 29 March 2022

    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… More >

  • Open Access

    ARTICLE

    Efficient Numerical Scheme for the Solution of HIV Infection CD4+ T-Cells Using Haar Wavelet Technique

    Rohul Amin1, Şuayip Yüzbası2,*, Shah Nazir3

    CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.2, pp. 639-653, 2022, DOI:10.32604/cmes.2022.019154 - 14 March 2022

    Abstract In this paper, Haar collocation algorithm is developed for the solution of first-order of HIV infection CD4+ T-Cells model. In this technique, the derivative in the nonlinear model is approximated by utilizing Haar functions. The value of the unknown function is obtained by the process of integration. Error estimation is also discussed, which aims to reduce the error of numerical solutions. The numerical results show that the method is simply applicable. The results are compared with Runge-Kutta technique, Bessel collocation technique, LADM-Pade and Galerkin technique available in the literature. The results show that the Haar technique More >

  • Open Access

    ARTICLE

    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 - 10 January 2022

    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 More >

  • Open Access

    ARTICLE

    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 - 07 December 2021

    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 More >

Displaying 21-30 on page 3 of 93. Per Page