Islamic Azad University of ArakTheory of Approximation and Applications2538-221710220140801Reproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problemReproducing Kernel Hilbert Space(RKHS)
method for solving singular perturbed
initial value problem112524218ENSaeidAbbasbandyDepartment of Mathematics, Imam Khomeini International University,
Qazvin, 34149-16818, Iran.MohammadAslefallahDepartment of Mathematics, Imam Khomeini International University,
Qazvin, 34149-16818, Iran.Journal Article20160824In 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 signicance.<br />We compare our results with other paper. The comparison of the results with exact ones is made to<br />conrm the validity and eciency.http://msj.iau-arak.ac.ir/article_524218_cdf449ce11beab3ca8364a9348f32661.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221710220140801On the rank of certain parametrized elliptic curvesOn the rank of certain parametrized
elliptic curves1322524219ENAliHadavandaDepartment of mathematics, Arak Branch, Islamic Azad university, Arak,
Iran.Journal Article20160824In 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.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221710220140801Approximate fixed point theorems for Geraghty-contractionsApproximate fixed point theorems for Geraghty-contractions2332515060ENُS. A. MMohsenalhoseiniValie-Asr UniversityHMazaheriIslamic Azad University of YazdJournal Article20150422The purpose of this paper is to obtain necessary and suffcient conditions<br />for existence approximate fixed point on Geraghty-contraction. In this paper,<br />denitions of approximate -pair fixed 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.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221710220140801FIXED POINT TYPE THEOREM IN S-METRIC SPACESFIXED POINT TYPE THEOREM IN S-METRIC SPACES3341515032ENJavadMojaradi-AfraInstitute of Mathematics, National Academy of Sciences of RA0000-0002-7097-6071Journal Article20150917 A variant of fixed point theorem is proved in the setting of S-metric spaceshttp://msj.iau-arak.ac.ir/article_515032_58f84a183e88d6f22157c1adf5688aea.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221710220140801A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functionsA meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis
functions4359522775ENJinoosNazariDepartment of Mathematics, Islamic Azad University, Khorasgan(Isfahan) BranchHomaAlmasiehDepartment of Mathematics, Khorasgan (Isfahan) Branch, Islamic
Azad UniversityJournal Article20151112In 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.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221710220140801Analytical solution of the Hunter-Saxton equation using the reduced dierential transform methodAnalytical solution of the Hunter-Saxton
equation using the reduced dierential
transform method6173524887ENH.RouhparvarDepartment of Mathematics, College of Technical and Engineering, Saveh
Branch, Islamic Azad University, Saveh, IranJournal Article20150719In this paper, the reduced dierential transform method is investigated for<br />a nonlinear partial dierential 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 dierential equations without<br />requiring linearization, discretization, or perturbation. It is a semi analytical-<br />numerical method that formulizes Taylor series in a very dierent manner.<br />The numerical results denote that reduced dierential transform method is<br />ecient and accurate for Hunter-Saxton equation.http://msj.iau-arak.ac.ir/article_524887_2aa61dc1b408b2d578f53d2e42bc3414.pdf