eng
Islamic Azad University
Theory of Approximation and Applications
2538-2217
2538-2217
2014-08-01
10
2
1
12
524218
مقاله های تحقیقی
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
Saeid Abbasbandy
1
Mohammad Aslefallah
2
Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.
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.
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_cdf449ce11beab3ca8364a9348f32661.pdf
Reproducing Kernel Hilbert Space(RKHS), Gram-Schmidt
orthogonalization process, Singular initial value problems
eng
Islamic Azad University
Theory of Approximation and Applications
2538-2217
2538-2217
2014-08-01
10
2
13
22
524219
مقاله های تحقیقی
On the rank of certain parametrized elliptic curves
On the rank of certain parametrized
elliptic curves
Ali Hadavand
hadavand@iau-arak.ac.ir
1
aDepartment of mathematics, Arak Branch, Islamic Azad university, Arak, Iran.
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.
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_a352fe09e5525c025e279f3f8001b001.pdf
Elliptic Curve
Selmer Group
eng
Islamic Azad University
Theory of Approximation and Applications
2538-2217
2538-2217
2014-08-01
10
2
23
32
515060
مقاله های تحقیقی
Approximate fixed point theorems for Geraghty-contractions
Approximate fixed point theorems for Geraghty-contractions
ُS. A. M Mohsenalhoseini
mohsenhosseini@yazd.ac.ir; amah@vru.ac.ir
1
H Mazaheri
2
Valie-Asr University
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.
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.
http://msj.iau-arak.ac.ir/article_515060_057cdb53815150301cc1de119411ec59.pdf
Approximate fixed point
Approximate-pair fixed point
Geraghty-contraction
Approximate fixed point
Approximate-pair fixed point
Geraghty-contraction
eng
Islamic Azad University
Theory of Approximation and Applications
2538-2217
2538-2217
2014-08-01
10
2
33
41
515032
مقاله های تحقیقی
FIXED POINT TYPE THEOREM IN S-METRIC SPACES
FIXED POINT TYPE THEOREM IN S-METRIC SPACES
Javad Mojaradi-Afra
mojarrad.afra@gmail.com
1
Institute of Mathematics, National Academy of Sciences of RA
A variant of fixed point theorem is proved in the setting of S-metric spaces
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
S-metric spaces
Coupled coincidence fixed point
k-contraction condition
eng
Islamic Azad University
Theory of Approximation and Applications
2538-2217
2538-2217
2014-08-01
10
2
43
59
522775
مقاله های تحقیقی
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
Jinoos Nazari
jinoosnazari@yahoo.com
1
Homa Almasieh
halmasieh@yahoo.co.uk
2
Department of Mathematics, Islamic Azad University, Khorasgan(Isfahan) Branch
Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad University
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.
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.
http://msj.iau-arak.ac.ir/article_522775_a6d67b27f5015bb884501bc3fb86794a.pdf
Nonlinear Volterra-Fredholm integral equation
Strictly positive
definite functions
Inverse multiquadrics
Hyperbolic secant
Nonlinear Volterra-Fredholm integral equation
Strictly positive
definite functions
Inverse multiquadrics
Hyperbolic secant
eng
Islamic Azad University
Theory of Approximation and Applications
2538-2217
2538-2217
2014-08-01
10
2
61
73
524887
مقاله های تحقیقی
Analytical solution of the Hunter-Saxton equation using the reduced dierential transform method
Analytical solution of the Hunter-Saxton
equation using the reduced dierential
transform method
H. Rouhparvar
rouhparvar59@gmail.com
1
Department of Mathematics, College of Technical and Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran
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.
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_2aa61dc1b408b2d578f53d2e42bc3414.pdf
Reduced differential transform method, Hunter-Saxton
equation, Taylor series