1394
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2
0
0
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
1
2
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.
1
12
Saeid
Abbasbandy
Saeid
Abbasbandy
Department of Mathematics, Imam Khomeini International University,
Qazvin, 34149-16818, Iran.
Department of Mathematics, Imam Khomeini
ایران
Mohammad
Aslefallah
Mohammad
Aslefallah
Department of Mathematics, Imam Khomeini International University,
Qazvin, 34149-16818, Iran.
Department of Mathematics, Imam Khomeini
ایران
[[1] S. Abbasbandy, B. Azarnavid, M.S. Alhuthali, A shooting reproducing##kernel Hilbert space method for multiple solutions of nonlinear boundary##value problems,Journal of Computational and Applied Mathematics, 279##(2015), 293-305.##[2] S. Abbasbandy, B. Azarnavid, Some error estimates for the reproducing##kernel Hilbert spaces method, Journal of Computational and Applied##Mathematics, 296 (2016) 789-797.##[3] B. Azarnavid, F. Parvaneh, S. Abbasbandy, Picard-Reproducing Kernel##Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-##Emden Type Equations, Mathematical Modelling and Analysis, 20(6)##(2015) 754-767.##[4] M. Cui, Y. Lin, Nonlinear numerical analysis in the reproducing kernel##space, Nova Science Pub. Inc., Hauppauge, 2009.##[5] Ghazala Akram, Hamood Ur Rehman, Solution of First Order Singularly##Perturbed Initial Value Problem in Reproducing Kernel Hilbert Space,##European Journal of Scientic Research, 53(4) (2011) 516-523.##[6] S. Gh. Hosseini, S. Abbasbandy, Solution of Lane-Emden Type Equations##by Combination of the Spectral Method and Adomian Decomposition##Method, Mathematical Problems in Engineering, Vol. 2015, Article ID##534754, 10 pages, 2015.##[7] S. Iqbal, A. Javed , Application of optimal homotopy asymptotic method##for the analytic solution of singular Lane-Emden type equation, Applied##Mathematics and Computation, 217 (2011) 7753-7761.##]
On the rank of certain parametrized elliptic curves
On the rank of certain parametrized
elliptic curves
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1
2
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.
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22
Ali
Hadavand
Ali
Hadavand
aDepartment of mathematics, Arak Branch, Islamic Azad university, Arak,
Iran.
aDepartment of mathematics, Arak Branch,
ایران
hadavand@iau-arak.ac.ir
[[1] J.S. Chahal, Topics in number theory, Kluwer Academic/Plenum##Publisher, 1988.##[2] J. E. Cremona, Algorithms of modular elliptic curves, Cambridge##University Press, 1997.##[3] A.J. Hollier, B. K. Spearman and Q. Yang, On the rank and integral points##of Elliptic Curves y2 = x3 - px, Int. J. Algebra, 3 ( 2009), no. 8, 401-406.##[4] T. Kudo and K. Motose, On Group structures of some special elliptic##curves,Math. J. Okayama Univ. 47 (2005), 81-84.##[5] S. Schmitt, Computing of the Selmer groups of certain parametrized##elliptic curves, Acta Arithmetica. LXXVIII (1997) 241{254.##[6] J. H. Silverman, The Arithmetic of Elliptic curves, GTM 106. Springer-##Verlage, New York, 1986.##[7] J. H. Silverman and J. Tate, Rational Points on Elliptic curves, Springer-##Verlage, New York, 1994.##[8] R. J. Stroeker and J. Top, On the equation y2 = (X +p)(X2 +p2), Rocky##Mountain J. Math. 27 (1994), 1135{1161.##[9] P. G. Walsh, Maximal Ranks and Integer Points on a Family of Elliptic##Curves,Glasnik Mathematicki. 44 (2009), 83-87.##]
Approximate fixed point theorems for Geraghty-contractions
Approximate fixed point theorems for Geraghty-contractions
1
1
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.
2
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.
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32
ُS. A. M
Mohsenalhoseini
ُS. A. M
Mohsenalhoseini
Valie-Asr University
Valie-Asr University
ایران
mohsenhosseini@yazd.ac.ir; amah@vru.ac.ir
H
Mazaheri
H
Mazaheri
Islamic Azad University of Yazd
Islamic Azad University of Yazd
ایران
Approximate fixed point
Approximate-pair fixed point
Geraghty-contraction
[[1] M. Berinde, Approximate Fixed Point Theorems,"Mathematica, vol. LI,##no. 1, 2006.##[2] M. Geraghty, On contractive mappings," Proc. Amer. Math. Soc. 40##(1973) 604-608.##[3] Jingling Zhang, Yongfu Su, Qingqing Cheng, Best proximity point##theorems for generalized contractions in partially ordered metric spaces,"##Fixed Point Theory and Applications 2013, 2013-200. ##[4] J. Caballero et al., A best proximity point theorem for Geraghty-##contractions, Fixed Point Theory and Applications 2012, 2012-231.##[5] S.A.M. Mohsenalhosseini, H. Mazaheri, Fixed Point For completely norm##Space and map T, Mathematica Moravica. Vol. 16-2 (2012), 25-35.##[6] S. A. M. Mohsenalhosseini, H. Mazaheri, M. A. Dehghan, Approximate Best##Proximity Pairs in Metric Space, Abstract and Applied Analysis, Volume##2011, Article ID 596971, 9 pages.##]
FIXED POINT TYPE THEOREM IN S-METRIC SPACES
FIXED POINT TYPE THEOREM IN S-METRIC SPACES
1
1
2
A variant of fixed point theorem is proved in the setting of S-metric spaces
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41
Javad
Mojaradi-Afra
Javad
Mojaradi-Afra
Institute of Mathematics, National Academy of Sciences of RA
Institute of Mathematics, National Academy
ایران
mojarrad.afra@gmail.com
[[1] T.G Bhaskar and G.V.Lakshmikantham . Fixed point theorems in partially ordered##metric spaces and applications, Nonlinear Analysis 65,(2006), 1379-1393.##[2] B.C. Dhage, Generalized metric spaces mappings with fixed point, Bull. Calcutta##Math. Soc. 84 (1992), 329-336.##[3] S. Gahler, 2-metrische Raume und iher topoloische Struktur, Math. Nachr. 26##(1963), 115- 148.##[4] V.Lakshmikantham, and Lj.B.Ciric, Coupled fixed point theorems for nonlinear##contrac- tions in partially ordered metric spaces, Nonlinear Analysis 70,##(2009),4341-4349.##[5] S. G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General##Topology and Applications, Ann. New York Acad. Sci. 728 (1994), 183-197. ##[6] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear##Convex Anal. 7 (2006), 289-297.##[7] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorem in Smetric##spaces, Mat. Vesnik 64 (2012), 258-266.##[8] S. Sedghi, N. Shobe, H. Zhou, A common fixed point theorem in D-metric spaces,##Fixed Point Theory Appl. Vol. 2007, Article ID 27906, 13 pages.##[9] W. Shatanawi, Fixed point theory for contractive mappings satisfying Φ-maps in##G-metric spaces, Fixed Point Theory Appl. Vol. 2010, Article ID 181650.##[10] W. Shatanawi, Coupled fixed point theorems in generalized metric spaces,##Hacettepe J. Math. Stat. 40 (3) (2011), 441-447.##]
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
1
1
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.
2
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.
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59
Jinoos
Nazari
Jinoos
Nazari
Department of Mathematics, Islamic Azad University, Khorasgan(Isfahan) Branch
Department of Mathematics, Islamic Azad University
ایران
jinoosnazari@yahoo.com
Homa
Almasieh
Homa
Almasieh
Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic
Azad University
Department of Mathematics, Khorasgan (Isfahan)
ایران
halmasieh@yahoo.co.uk
Nonlinear Volterra-Fredholm integral equation
Strictly positive
definite functions
Inverse multiquadrics
Hyperbolic secant
[[1] H. Almasieh, J. Nazari Meleh, Numerical solution of a class of mixed##two-dimensional nonlinear Volterra-Fredholm integral equations using##multiquadric radial basis functions, Comput. Appl. Math. 260 (2014) 173{##[2] A. Alipanah, M. Dehghan, Numerical solution of the nonlinear Fredholm##integral equations by positive denite functions, Appl. Math. Comput. 190##(2007) 1754{1761.##[3] B. J. C. Baxter, The interpolation theory of Radial Basis Functions,##Cambridge University, 1992.##[4] A. H. D. Cheng, M. A. Galberg, E. J. Kansa, Q. Zammito, Exponential##convergence and H-c multiquadratic collocation method for partial##dierential equations, Numer. Meth. Part. D. E. 19 (2003) 571{594.##[5] W. Cheney, W. Light, A course in approximation theory, New York, 1999.##[6] K. B. Datta, B. M. Mohan, Orthogonal Functions in System and Control,##World Scientic, Singapore, 1995.##[7] G. N. Elnagar, M. A. Kazemi, Pseudospectral Legendre-based optimal##computaion of nonlinear constrained variational problems, J. Comput.##Appl. Math. 88 (1997) 363{375.##[8] G. N. Elnagar, M. Razzaghi, A collocation-type method for linear##quadratic optimal control problems, Optim. Control. Appl. Meth. 18##(1998) 227{235. ##[9] R. E. Garlson, T .A. Foly, The parameter R2 in multiquadratic##interpolation, Comput. Math. Appl. 21 (1991) 29{42.##[10] M. A. Galberg, Some recent results and proposals for the use of radial basis##functions in the BEM, Eng. Anal. Bound. Elem. 23(4) (1999) 285{296.##[11] C. Kui-Fang, Strictly positive denite functions, J. Approx. Theory 87##(1996) 148{15.##[12] K. Maleknejad, Y. Mahmoudi, Numerical solution of linear Fredholm##integral equations by using Hybrid Taylor and Block-Pulse functions,Appl.##Math. Comput. 149 (2004) 799{806.##[13] K. Parand, J. A. Rad, Numerical solution of nonlinear Volterra-Fredholm-##Hammerstein integral equations via collocation method based on radial##basis functions, Appl. Math. Comput. 218 (2012) 5292{5309.##[14] M. Razzaghi, S. Youse, Legendre wavelets mehod for the nonlinear##Volterra-Fredholm integral equations, Math. Comput. Simul. 70 (2005)##[15] J. Rashidinia, M. Zarebnia, New approach for numerical solution of##Hammerstein integral equations, Appl. Math. Comput. 185 (2007) 147{##[16] M. H. Reihani, Z. Abadi, Rationalized Haar function method for solving##Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200##(2007) 12{20.##[17] J. Shen, T. Tang, High order numerical Methods and Algorithms, Abstract##and Applied Analysis, Chinese Science Press, 2005.##[18] A. E. Tarwater, A parameter study of Hardy's multiquadratic method for##scattered data interpolation, Report UCRL - 53670, Lawrence Livermore##National Laboratory, 1985.##[19] S. Yalinbas, Taylor polynomial solution of nonlinear Volterra-Fredholm##integral equations, Appl. Math. Comput. 127 (2002) 195{206.##]
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
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1
2
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.
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73
H.
Rouhparvar
H.
Rouhparvar
Department of Mathematics, College of Technical and Engineering, Saveh
Branch, Islamic Azad University, Saveh, Iran
Department of Mathematics, College of Technical
ایران
rouhparvar59@gmail.com
[[1] I. H. Abdel-Halim Hassan, Vedat Suat Ertrk, Applying dierential##transformation method to the one-dimensional planar Bratu problem,##Int. J. Contemp. Math. Sciences, 2(30) (2007), 1493-1504.##[2] I. H. Abdel-Halim Hassan, Dierential transformation technique for##solving higher-order initial value problems, Appl. Math. Comput., 154##(2004), 299-311.##[3] I. H. Abdel-Halim Hassan, Application to dierential transformation##method for solving systems of dierential equations, Appl. Math.##Modell., 32(12) (2008), 2552-2559.##[4] A. Arikoglu and I. Ozkol, Solution of boundary value problems for##integro-dierential equations by using dierential transform method,##Appl. Math. Comput., 168 (2005), 1145-1158.##[5] F. Ayaz, Solutions of the systems of dierential equations by##dierential transform method, Appl. Math. Comput., 147 (2004), 547-##[6] F. Ayaz, On the two-dimensional dierential transform method,##Appl. Math. Comput., 143 (2003) 361-374.##[7] R. Camassa and D. D. Holm, An integrable shallow water equation##with peaked solitons, Phys. Rev. Lett., 71 (1993), 1661-1664.##[8] C. K. Chen and S. H. Ho, Application of dierential transformation##to eigenvalue problems, Appl. Math. Comput., 79 (1996), 173-188.##[9] A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal##shallow water equations, Acta Mathematics, 181 (1998), 229-243. ##[10] J. K. Hunter and R. Saxton, Dynamics of director elds, SIAM J.##Appl. Math, 51 (1991), 1498-1521.##[11] M. J. Jang and C. L. Chen, Analysis of the response of a##strongly nonlinear damped system using a dierential transformation##technique, Appl. Math. Comput., 88 (1997), 137-151.##[12] M. J. Jang and C. K. Chen, Two-dimensional dierential##transformation method for partial dierantial equations, Appl. Math.##Copmut., 121 (2001), 261-270.##[13] R. S. Johnson and Camassa-Holm, Korteweg-de Vries and related##models for water waves, J. Fluid Mech., 455 (2002), 63-82.##[14] F. Kangalgil and F. Ayaz, Solitary wave solutions for the KdV and##mKdV equations by dierential transform method, Chaos Solitons &##Fractals, 41 (2009), 464-472.##[15] Y. Keskin and G. Oturanc, Reduced Dierential Transform Method##for Partial Dierential Equations, International Journal of Nonlinear##Sciences and Numerical Simulation, 10 (6) (2009), 741-749.##[16] Y. Keskin and G. Oturanc, Reduced dierential transform method##for solving linear and nonlinear wave equations, Iranian Journal of##Science & Technology, Transaction A, 34(A2) 2010, 113-122.##[17] Y. Keskin and G. Oturanc, Reduced Dierential Transform Method##for fractional partial dierential equations, Nonlinear Science Letters##A, 1(2) (2010), 61-72.##[18] Y. Keskin, Ph.D. Thesis, Selcuk University (to appear).##[19] H. Liu and Yongzhong Song, Dierential transform method##applied to high index dierential algebraic equations, Appl. Math.##Comput.,184 (2007), 748-753.##[20] J. K. Zhou, Dierential transformation and its application for##electrical circuits, Huarjung University PressWuuhahn, China (1986),##(in Chinese).##]