Islamic Azad University of Arak Theory of Approximation and Applications 2538-2217 10 2 2014 08 01 Reproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problem Reproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problem 1 12 524218 EN Saeid Abbasbandy Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran. Mohammad Aslefallah Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran. Journal Article 2016 08 24 In this paper, a numerical scheme for solving singular initial/boundary value problems presented.<br />By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,<br />this method obtained to approximated solution. Numerical examples are given to demonstrate the<br />accuracy of the present method. The result obtained by the method and the exact solution are found<br />to be in good agreement with each other and it is noted that our method is of high signi cance.<br />We compare our results with other paper. The comparison of the results with exact ones is made to<br />con rm the validity and eciency. http://msj.iau-arak.ac.ir/article_524218_cdf449ce11beab3ca8364a9348f32661.pdf
Islamic Azad University of Arak Theory of Approximation and Applications 2538-2217 10 2 2014 08 01 On the rank of certain parametrized elliptic curves On the rank of certain parametrized elliptic curves 13 22 524219 EN Ali Hadavand aDepartment of mathematics, Arak Branch, Islamic Azad university, Arak, Iran. Journal Article 2016 08 24 In this paper the family of elliptic curves over Q given by the equation Ep :<br />Y<sup>2</sup> = (X - p)<sup>3</sup> + X<sup>3</sup> + (X + p)<sup>3</sup> where p is a prime number, is studied. It<br />is shown that the maximal rank of the elliptic curves is at most 3 and some<br />conditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 or<br />rank(Ep(Q))≥2 are given. http://msj.iau-arak.ac.ir/article_524219_a352fe09e5525c025e279f3f8001b001.pdf
Islamic Azad University of Arak Theory of Approximation and Applications 2538-2217 10 2 2014 08 01 Approximate fi xed point theorems for Geraghty-contractions Approximate fi xed point theorems for Geraghty-contractions 23 32 515060 EN ُS. A. M Mohsenalhoseini Valie-Asr University H Mazaheri Islamic Azad University of Yazd Journal Article 2015 04 22 The purpose of this paper is to obtain necessary and suffcient conditions<br />for existence approximate fi xed point on Geraghty-contraction. In this paper,<br />de nitions of approximate -pair fi xed point for two maps T <sub>α</sub> , S<sub>α</sub> and their<br />diameters are given in a metric space. http://msj.iau-arak.ac.ir/article_515060_057cdb53815150301cc1de119411ec59.pdf
Islamic Azad University of Arak Theory of Approximation and Applications 2538-2217 10 2 2014 08 01 FIXED POINT TYPE THEOREM IN S-METRIC SPACES FIXED POINT TYPE THEOREM IN S-METRIC SPACES 33 41 515032 EN Javad Mojaradi-Afra Institute of Mathematics, National Academy of Sciences of RA 0000-0002-7097-6071 Journal Article 2015 09 17   A variant of fixed point theorem is proved in the setting of S-metric spaces http://msj.iau-arak.ac.ir/article_515032_58f84a183e88d6f22157c1adf5688aea.pdf
Islamic Azad University of Arak Theory of Approximation and Applications 2538-2217 10 2 2014 08 01 A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions 43 59 522775 EN Jinoos Nazari Department of Mathematics, Islamic Azad University, Khorasgan(Isfahan) Branch Homa Almasieh Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad University Journal Article 2015 11 12 In this paper, an effective technique is proposed to determine the<br />numerical solution of nonlinear Volterra-Fredholm integral<br />equations (VFIEs) which is based on interpolation by the hybrid of<br />radial basis functions (RBFs) including both inverse multiquadrics<br />(IMQs), hyperbolic secant (Sechs) and strictly positive definite<br />functions. Zeros of the shifted Legendre polynomial are used as<br />the collocation points to set up the nonlinear systems. The<br />integrals involved in the formulation of the problems are<br />approximated based on Legendre-Gauss-Lobatto integration rule.<br />This technique is so convenience to implement and yields very<br />accurate results compared with the other basis. In addition a<br />convergence theorem is proved to show the stability of this<br />technique. Illustrated examples are included to confirm the<br />validity and applicability of the proposed method. The comparison<br />of the errors is implemented by the other methods in references<br />using both inverse multiquadrics (IMQs), hyperbolic secant (Sechs)<br />and strictly positive definite functions. http://msj.iau-arak.ac.ir/article_522775_a6d67b27f5015bb884501bc3fb86794a.pdf
Islamic Azad University of Arak Theory of Approximation and Applications 2538-2217 10 2 2014 08 01 Analytical solution of the Hunter-Saxton equation using the reduced di erential transform method Analytical solution of the Hunter-Saxton equation using the reduced di erential transform method 61 73 524887 EN H. Rouhparvar Department of Mathematics, College of Technical and Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran Journal Article 2015 07 19 In this paper, the reduced di erential transform method is investigated for<br />a nonlinear partial di erential equation modeling nematic liquid crystals, it<br />is called the Hunter-Saxton equation. The main advantage of this method<br />is that it can be applied directly to nonlinear di erential equations without<br />requiring linearization, discretization, or perturbation. It is a semi analytical-<br />numerical method that formulizes Taylor series in a very di erent manner.<br />The numerical results denote that reduced di erential transform method is<br />ecient and accurate for Hunter-Saxton equation. http://msj.iau-arak.ac.ir/article_524887_2aa61dc1b408b2d578f53d2e42bc3414.pdf