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  • Open Access

    ARTICLE

    Numerical Solution of System of N–Coupled Nonlinear Schrödinger Equations via Two Variants of the Meshless Local Petrov–Galerkin (MLPG) Method

    M. Dehghan1, M. Abbaszadeh2, A. Mohebbi3

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 399-444, 2014, DOI:10.3970/cmes.2014.100.399

    Abstract In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis functions (RBFs) collocation methodology. We introduce the moving least squares (MLS) approximation and radial point interpolation method (RPIM) with their shape functions, separately. It should be noted that the shape functions of RPIM unlike the shape functions of the… More >

  • Open Access

    ARTICLE

    Some Geometric Invariants of Pseudo-Spherical Evolutes in the Hyperbolic 3-Space

    H. S. Abdel-Aziz1, M. Khalifa Saad1,2,*, A. A. Abdel-Salam1

    CMC-Computers, Materials & Continua, Vol.57, No.3, pp. 389-415, 2018, DOI:10.32604/cmc.2018.02149

    Abstract In this paper, we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space. We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group. Besides, we defray with illustration some computational examples in support our main results. More >

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