Islamic Azad University
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
1
12
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.
In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agreement with each other and it is noted that our method is of high signicance.We compare our results with other paper. The comparison of the results with exact ones is made toconrm the validity and eciency.
http://msj.iau-arak.ac.ir/article_524218.html
http://msj.iau-arak.ac.ir/article_524218_cdf449ce11beab3ca8364a9348f32661.pdf
Islamic Azad University
Theory of Approximation and Applications
2538-2217
10
2
2014
08
01
On the rank of certain parametrized elliptic curves
13
22
EN
Ali
Hadavand
aDepartment of mathematics, Arak Branch, Islamic Azad university, Arak,
Iran.
hadavand@iau-arak.ac.ir
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
http://msj.iau-arak.ac.ir/article_524219.html
http://msj.iau-arak.ac.ir/article_524219_a352fe09e5525c025e279f3f8001b001.pdf
Islamic Azad University
Theory of Approximation and Applications
2538-2217
10
2
2014
08
01
Approximate fixed point theorems for Geraghty-contractions
23
32
EN
ُS. A. M
Mohsenalhoseini
Valie-Asr University
mohsenhosseini@yazd.ac.ir; amah@vru.ac.ir
H
Mazaheri
Islamic Azad University of Yazd
The purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fixed point on Geraghty-contraction. In this paper,denitions of approximate -pair fixed point for two maps Tα , Sα and theirdiameters are given in a metric space.
Approximate fixed point,Approximate-pair fixed point,Geraghty-contraction
http://msj.iau-arak.ac.ir/article_515060.html
http://msj.iau-arak.ac.ir/article_515060_057cdb53815150301cc1de119411ec59.pdf
Islamic Azad University
Theory of Approximation and Applications
2538-2217
10
2
2014
08
01
FIXED POINT TYPE THEOREM IN S-METRIC SPACES
33
41
EN
Javad
Mojaradi-Afra
Institute of Mathematics, National Academy of Sciences of RA
mojarrad.afra@gmail.com
A variant of fixed point theorem is proved in the setting of S-metric spaces
http://msj.iau-arak.ac.ir/article_515032.html
http://msj.iau-arak.ac.ir/article_515032_58f84a183e88d6f22157c1adf5688aea.pdf
Islamic Azad University
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
43
59
EN
Jinoos
Nazari
Department of Mathematics, Islamic Azad University, Khorasgan(Isfahan) Branch
jinoosnazari@yahoo.com
Homa
Almasieh
Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic
Azad University
halmasieh@yahoo.co.uk
In this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocation points to set up the nonlinear systems. Theintegrals involved in the formulation of the problems areapproximated based on Legendre-Gauss-Lobatto integration rule.This technique is so convenience to implement and yields veryaccurate results compared with the other basis. In addition aconvergence theorem is proved to show the stability of thistechnique. Illustrated examples are included to confirm thevalidity and applicability of the proposed method. The comparisonof the errors is implemented by the other methods in referencesusing both inverse multiquadrics (IMQs), hyperbolic secant (Sechs)and strictly positive definite functions.
Nonlinear Volterra-Fredholm integral equation,Strictly positive,definite functions,Inverse multiquadrics,Hyperbolic secant
http://msj.iau-arak.ac.ir/article_522775.html
http://msj.iau-arak.ac.ir/article_522775_a6d67b27f5015bb884501bc3fb86794a.pdf
Islamic Azad University
Theory of Approximation and Applications
2538-2217
10
2
2014
08
01
Analytical solution of the Hunter-Saxton equation using the reduced dierential transform method
61
73
EN
H.
Rouhparvar
Department of Mathematics, College of Technical and Engineering, Saveh
Branch, Islamic Azad University, Saveh, Iran
rouhparvar59@gmail.com
In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method that formulizes Taylor series in a very dierent manner.The numerical results denote that reduced dierential transform method isecient and accurate for Hunter-Saxton equation.
http://msj.iau-arak.ac.ir/article_524887.html
http://msj.iau-arak.ac.ir/article_524887_2aa61dc1b408b2d578f53d2e42bc3414.pdf