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  • Open Access


    Existence of Approximate Solutions to Nonlinear Lorenz System under Caputo-Fabrizio Derivative

    Khursheed J. Ansari1, Mustafa Inc2,3,4,*, K. H. Mahmoud5,*, Eiman6

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1669-1684, 2023, DOI:10.32604/cmes.2022.022971

    Abstract In this article, we developed sufficient conditions for the existence and uniqueness of an approximate solution to a nonlinear system of Lorenz equations under Caputo-Fabrizio fractional order derivative (CFFD). The required results about the existence and uniqueness of a solution are derived via the fixed point approach due to Banach and Krassnoselskii. Also, we enriched our work by establishing a stable result based on the Ulam-Hyers (U-H) concept. Also, the approximate solution is computed by using a hybrid method due to the Laplace transform and the Adomian decomposition method. We computed a few terms of the required solution through the… More >

  • Open Access


    Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

    K. A. Gepreel1,2, A. M. S. Mahdy1,2,*, M. S. Mohamed1,3, A. Al-Amiri4

    CMC-Computers, Materials & Continua, Vol.61, No.3, pp. 979-994, 2019, DOI:10.32604/cmc.2019.07701

    Abstract In this paper, we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model. The reduced differential transforms method (RDTM) is one of the interesting methods for finding the approximate solutions for nonlinear problems. We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model. We discuss the numerical results at some special values of parameters in the approximate solutions. We use the computer software package such… More >

  • Open Access


    Approximation of Unit-Hypercubic Infinite Noncooperative Game Via Dimension-Dependent Samplings and Reshaping the Player’s Payoffs into Line Array for the Finite Game Simplification

    Vadim V. Romanuke1

    CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.2, pp. 113-134, 2015, DOI:10.3970/cmes.2015.108.113

    Abstract The problem of solving infinite noncooperative games approximately is considered. The game may either have solution or have no solution. The existing solution may be unknown as well. Therefore, an approach of obtaining the approximate solution of the infinite noncooperative game on the unit hypercube is suggested. The unit-hypercubic game isomorphism to compact infinite noncooperative games allows to disseminate the approximation approach on a pretty wide class of noncooperative games. The approximation intention is in converting the infinite game into a finite one, whose solution methods are easier rather than solving infinite games. The conversion starts with sampling the players’… More >

  • Open Access


    Particle-based Simulations of Flows with Free Surfaces Using Hyperbolic-typeWeighting Functions

    K. Kakuda1, Y. Hayashi1, J. Toyotani1

    CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.4, pp. 229-249, 2014, DOI:10.3970/cmes.2014.103.229

    Abstract In this paper, we present the application of the particle-based simulations to complicated fluid flow problem with free surfaces. The particle approach is based on the MPS (Moving Particle Simulation) method using hyperbolic-type weighting function to stabilize the spurious oscillatory solutions for solving the Poisson equation with respect to the pressure fields. The hyperbolic-type weighting function is constructed by differentiating the characteristic function based on neural network framework. The weighting function proposed herein is collaterally applied to the kernel function in the SPH-framework. Numerical results demonstrate the workability and validity of the present MPS approach through the dambreaking flow problem. More >

  • Open Access


    Numerical Approximate Solutions of Nonlinear Fredholm Integral Equations of Second Kind Using B-spline Wavelets and Variational Iteration Method

    P. K. Sahu1, S. Saha Ray1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.2, pp. 91-112, 2013, DOI:10.3970/cmes.2013.093.091

    Abstract In this paper, nonlinear integral equations have been solved numerically by using B-spline wavelet method and Variational Iteration Method (VIM). Compactly supported semi-orthogonal linear B-spline scaling and wavelet functions together with their dual functions are applied to approximate the solutions of nonlinear Fredholm integral equations of second kind. Comparisons are made between the variational Iteration Method (VIM) and linear B-spline wavelet method. Several examples are presented to compare the accuracy of linear B-spline wavelet method and Variational Iteration Method (VIM) with their exact solutions. More >

  • Open Access


    Application of Residual Correction Method on Error Analysis of Numerical Solution on the non-Fourier Fin Problem

    Hsiang-Wen Tang, Cha’o-Kung Chen1, Chen-Yu Chiang

    CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.1, pp. 95-106, 2010, DOI:10.3970/cmes.2010.065.095

    Abstract Up to now, solving some nonlinear differential equations is still a challenge to many scholars, by either numerical or theoretical methods. In this paper, the method of the maximum principle applied on differential equations incorporating the Residual Correction Method is brought up and utilized to obtain the upper and lower approximate solutions of nonlinear heat transfer problem of the non-Fourier fin. Under the fundamental of the maximum principle, the monotonic residual relations of the partial differential governing equation are established first. Then, the finite difference method is applied to discretize the equation, converting the differential equation into the mathematical programming… More >

  • Open Access


    Approximate Solution of an Inverse Problem for a Non-Stationary General Kinetic Equation

    Mustafa Yidiz1, Bayram Heydarov2, İsmet Gölgeleyen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.3, pp. 255-264, 2010, DOI:10.3970/cmes.2010.062.255

    Abstract We investigate the solvability of an inverse problem for the non-stationary general kinetic equation. We also obtained the approximate solution of this problem by using symbolic computation. A comparison between the approximate solution and the exact solution of the problem is presented. More >

  • Open Access


    On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

    K. Vijayakumar1

    CMC-Computers, Materials & Continua, Vol.34, No.1, pp. 1-25, 2013, DOI:10.3970/cmc.2013.034.001

    Abstract A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a… More >

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