2017
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Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations
Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations
2
2
Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this method. Aboodh transform was introducedby Khalid Aboodh to facilitate the process of solving ordinary and partialdifferential equations in the time domain.
1
Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this method. Aboodh transform was introducedby Khalid Aboodh to facilitate the process of solving ordinary and partialdierential equations in the time domain.
1
12
Khalid
Aboodh
Khalid
Aboodh
Department of Mathematics Omdurman Islamic University (http: //www. fst. oiu. edu. sd) sudan
Department of Mathematics Omdurman Islamic
Iran
khalidmath78@yahoo.com
Aboodh transform
Homotopy perturbation method
Nonlinear partial differential equations
[[1]S. lslam, Yasir Khan, Naeem Faraz and Francis Austin (2010),##Numerical Solution of Logistic Dierential Equations by using the Laplace##Decomposition Method, World Applied Sciences Journal 8(9):1100-1105.##[2]Nuran Guzel and Muhammet Nurulay (2008), Solution of Shi Systems##By using Dierential Transform Method, Dunlupinar universities Fen##Bilimleri Enstitusu Dergisi, ISSN 1302-3055, PP. 49-59.##[3]Shin- Hsiang Chang , I-Ling Chang (2008), A new algorithm for##calculating one-dimensional dierential transform of nonlinear functions,##Applied Mathematics and Computation 195 ,799-808.##[4]Khalid Suliman Aboodh, The New Integral Transform Aboodh##Transform", GlobalJournal of Pure and Applied Mathematics ISSN 09731768##Volume 9, Number 1 (2013), pp. 35-43.##[5]Tarig M. Elzaki (2011), The New Integral Transform "Elzaki ransform?##Global Journal of Pure and Applied Mathematics, ISSN 09731768,Number##1, pp. 57-64.##[6]Tarig M. Elzaki and Salih M. Elzaki (2011), Application of New transform##?Elzaki Transform? to Partial Dierential Equations, Global Journal of##Pure and Applied Mathematics, ISSN 0973-1768,Number 1, pp.65-70.##[7]Tarig M. Elzaki and Salih M. Elzaki (2011), On the Connections between##Laplace and Elzaki transforms, Advances in Theoretical and Applied##Mathematics, ISSN 0973-4554 Volume 6, Number 1, pp. 1-11.##[8]Tarig M. Elzaki and Salih M. Elzaki (2011), On the Elzaki Transform and##Ordinary Dierential Equation With Variable Coecients, Advances in##Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6 Number##1, pp. 13-18.##[9]Lokenath Debnath and D. Bhatta (2006). Integral transform and their##Application second Edition,Chapman & Hall /CRC##[10]A.Kilicman and H.E.Gadain. (2009), An application of double Laplace##transform and Sumudu transform, Lobachevskii J. Math.30 (3) pp.214223.##[11]J. Zhang, (2007). A Sumudu based algorithm m for solving dierential##equations, Comp. Sci. J.Moldova 15(3), pp-303-313.##[12]Hassan Eltayeb and Adem kilicman, (2010), A Note on the Sumudu##Transforms and dierential Equations, Applied Mathematical Sciences,##VOL, 4, no.22,1089-1098##[13]Kilicman A.and H. ELtayeb. (2010), A note on Integral transform##and Partial Dierential Equation, Applied Mathematical Sciences,4(3),##PP.109-118.##[14]Hassan Eltayeh and Adem kilicman (2010), on Some Applications of a new##Integral Transform, Int.Journal of Math. Analysis, Vol, 4, no.3, 123-132.##[15]N.H. Sweilam, M.M. Khader (2009). Exact Solutions of some Capled##nonlinear partial dierential equations using the homotopy perturbation##method. Computers and Mathematics with Applications 58,2134-2141.##[16]P.R. Sharma and Giriraj Methi (2011). Applications of Homotopy##Perturbation method to Partial dierential equations. Asian Journal of##Mathematics and Statistics 4 (3): 140-150.##[17]M.A. Jafari, A. Aminataei (2010). Improved Homotopy Perturbation##Method. International Mathematical Forum, 5, no, 32, 1567-1579.##[18]Jagdev Singh, Devendra, Sushila. Homotopy Perturbation Sumudu##Transform Method for Nonlinear Equations. Adv. Theor. Appl. Mech.,##Vol. 4, 2011, no. 4, 165-175.##[19]Nuran Guzel and Muhammet Nurulay (2008), Solution of Shi Systems##By using Dierential Transform Method, Dunlupinar universities Fen##Bilimleri Enstitusu Dergisi, ISSN 1302-3055, PP. 49-59.##[20]Shin- Hsiang Chang , I-Ling Chang (2008), A new algorithm for##calculating one-dimensional dierential transform of nonlinear functions,##Applied Mathematics and Computation 195, 799-808.##[21]Hashim, I, Adomian decomposition method applied to the Lorenz system##chaos.08.135.##[22]Tarig M. Elzaki, Salih M. Elzaki, and Eman M. A. Hilal, (2012). Elzaki##and Sumudu Transforms for Solving Some Dierential Equations, Global##Journal of Pure and Applied Mathematics, ISSN 0973-1768, Volume 8,##Number 2, pp. 167-173.##[23]Tarig M. Elzaki, and Eman M. A. Hilal, (2012). Homotopy Perturbation##and Elzaki Transform for Solving Nonlinear Partial Differential Equations,##Mathematical Theory and Modeling , ISSN 2224-5804, Vol.2, No.3, 2012,##pp. 33-42.##]
Bifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations
Bifurcation Problem for Biharmonic
Asymptotically Linear Elliptic Equations
2
2
In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the problem has no solution even in the week sense.We also show that $lambda^{ast}=frac{lambda_{1}}{a}$ if$ lim_{trightarrow infty}f(t)-at=lgeq0$ and for $lambda< lambda^{ast}$, the solution is unique but for $l<0$ and $frac{lambda_{1}}{a}<lambda< lambda^{ast}$, the problem has two branches of solutions, where $lambda_{1}$ is the first eigenvalue associated to the problem.
1
In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the problem has no solution even in the week sense.We also show that $lambda^{ast}=frac{lambda_{1}}{a}$ if$ lim_{trightarrow infty}f(t)-at=lgeq0$ and for $lambda< lambda^{ast}$, the solution is unique but for $l<0$ and $frac{lambda_{1}}{a}<lambda< lambda^{ast}$, the problem has two branches of solutions, where $lambda_{1}$ is the first eigenvalue associated to the problem.
13
37
Makkia
Dammak
Makkia
Dammak
University of Tunis El Manar, Higher Institute of Medical Technologies of Tunis
09 doctor Zouhair Essafi Street 1006 Tunis,Tunisia
University of Tunis El Manar, Higher Institute
Iran
makkia.dammak@gmail.com
Majdi
El Ghord
Majdi
El Ghord
University of Tunis El Manar, Faculty of Sciences of Tunis, Campus Universities 2092 Tunis, Tunisia
University of Tunis El Manar, Faculty of
Iran
A Numerical Approach for Solving Forth Order Fuzzy Differential Equations Under Generalized Differentiability
A Numerical Approach for Solving Forth
Order Fuzzy Differential Equations Under
Generalized Differentiability
2
2
In this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. This method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . We investigate the existence and uniqueness of solutions. Finally anumerical example is presented to illustrate the accuracy of the new technique.
1
In this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. This method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . We investigate the existence and uniqueness of solutions. Finally anumerical example is presented to illustrate the accuracy of the new technique.
39
56
E.
Ahmadi
E
Ahmadi
Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad
University, Tehran, Iran
Department of Mathematics, Shahr-e-Qods Branch,
Iran
e.ahmadi@qodsiau.ac.ir
N.
Ahmadi
N.
Ahmadi
ِDepartment of Mathematics, Varamin-Pishva Branch, Islamic Azad
University, Varamin, Iran
ِDepartment of Mathematics, Varamin-Pishva
Iran
Higher Derivations Associated with the Cauchy-Jensen Type Mapping
Higher Derivations Associated with the
Cauchy-Jensen Type Mapping
2
2
Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation
2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R)
for all T,S,Rin K(H).
1
Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation
2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R)
for all T,S,Rin K(H).
57
68
Hamidreza
Reisi
حمیدرضا
رییسی
دانشجوی دکتری دانشگاه سمنان
دانشجوی دکتری دانشگاه سمنان
Iran
hamidreza.reisi@gmail.com
w_0-Nearest Points and w_0-Farthest Point in Normed Linear Spaces
ω_0-Nearest Points and ω_0-Farthest Point in Normed Linear Spaces
2
2
w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces
1
In this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. We shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.
69
79
Hamid
Mazaheri
حمید
مظاهری تهرانی
دانشگاه یزد
دانشگاه یزد
Iran
hmazaheri@yazd.ac.ir
The Study Properties of Subclass of Starlike Functions
The Study Properties of Subclass of Starlike
Functions
2
2
In this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk U.Such results as coecientinequalities. The results presented here would provide extensions of those givenin earlier works.
1
In this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk U.Such results as coecientinequalities. The results presented here would provide extensions of those givenin earlier works.
81
86
Mohammad
Taati
Mohammad
Taati
Department of Mathematics, Payame Noor University, P.O.Box
19395-3697, Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
m-taati@pnu.ac.ir
Elliptic Function Solutions of (2+1)-Dimensional Breaking Soliton Equation by Sinh-Cosh Method and Sinh-Gordon Expansion Method
Elliptic Function Solutions of
(2+1)-Dimensional Breaking Soliton
Equation by Sinh-Cosh Method and
Sinh-Gordon Expansion Method
2
2
In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.
1
In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.
87
98
Parvaneh
Nabipourkisomi
پروانه
نبی پور کیسمی
مدرس آموزشگاه
مدرس آموزشگاه
Iran
parvanehnabipour@yahoo.com
Analytic Solution of Fuzzy Second Order Differential Equations under H-Derivation
Analytic Solution of Fuzzy Second Order
Differential Equations under H-Derivation
2
2
In this paper, the solution of linear second order equations with fuzzy initialvalues are investigated. The analytic general solutions of them using a rstsolution is founded. The parametric form of fuzzy numbers to solve the secondorder equations is applied. The solutions are searched in four cases. Finallythe example is got to illustrate more and the solutions are shown in gures forfour cases.
1
In this paper, the solution of linear second order equations with fuzzy initialvalues are investigated. The analytic general solutions of them using a rstsolution is founded. The parametric form of fuzzy numbers to solve the secondorder equations is applied. The solutions are searched in four cases. Finallythe example is got to illustrate more and the solutions are shown in gures forfour cases.
99
115
Laleh
Hooshangian
Laleh
Hooshangian
Department of Mathematics, Dezful Branch, Islamic Azad University,
Dezful, Iran.
Department of Mathematics, Dezful Branch,
Iran
l-hooshangian@yahoo.com