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  • Open Access

    ARTICLE

    Application of the Fictitious Domain Method for Navier-Stokes Equations

    Almas Temirbekov1, Zhadra Zhaksylykova2,*, Yerzhan Malgazhdarov3, Syrym Kasenov1

    CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 2035-2055, 2022, DOI:10.32604/cmc.2022.027830 - 18 May 2022

    Abstract To apply the fictitious domain method and conduct numerical experiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different values of the iterative parameter τ and the small parameter ε are presented. A study of the auxiliary problem of the fictitious domain method for Navier-Stokes equations with continuation into a fictitious subdomain by higher coefficients with a small parameter is carried out. A generalized solution of the auxiliary problem of the fictitious domain method with continuation by higher coefficients with a small parameter is determined. After… More >

  • Open Access

    ARTICLE

    A Computational Analysis to Burgers Huxley Equation

    Muhammad Saqib1, Muhammad Shoaib Arif2,*, Shahid Hasnain3, Daoud S. Mashat4

    CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 2161-2183, 2021, DOI:10.32604/cmc.2021.014507 - 05 February 2021

    Abstract The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise, higher-order compact numerical scheme that results in truly outstanding accuracy at a given cost. The objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley (BH) equations. The proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities, and in a smooth flow region, it efficiently obtained a high-order accuracy. In particular, two classes of higher-order compact finite difference schemes are taken into account and… More >

  • Open Access

    ARTICLE

    Meshless Local Petrov-Galerkin and RBFs Collocation Methods for Solving 2D Fractional Klein-Kramers Dynamics Equation on Irregular Domains

    M. Dehghan1, M. Abbaszadeh2, A. Mohebbi3

    CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 481-516, 2015, DOI:10.3970/cmes.2015.107.481

    Abstract In the current paper the two-dimensional time fractional Klein-Kramers equation which describes the subdiffusion in the presence of an external force field in phase space has been considered. The numerical solution of fractional Klein-Kramers equation is investigated. The proposed method is based on using finite difference scheme in time variable for obtaining a semi-discrete scheme. Also, to achieve a full discretization scheme, the Kansa's approach and meshless local Petrov-Galerkin technique are used to approximate the spatial derivatives. The meshless method has already proved successful in solving classic and fractional differential equations as well as for… More >

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