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2020
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Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales
Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales
en
en
In this paper, we define \(\Psi \)-boundedness on time scales and we present necessary and sufficient conditions for the existence of at least one \(\Psi\)-bounded solution for the linear non-homogeneous matrix system \(x^{\Delta}=A(t)x + f(t)\), where f(t) is a \(\Psi\)-bounded matrix valued function on \({T}\) assuming that \(f\) is a Lebesgue \(\Psi\)-delta integrable function on time scale \({T}\). Finally we give a result in connection with the asymptotic behavior of the \(\Psi\)-bounded solutions of this system.
1
13
Kasi Viswanadh V.
Kanuri
USA
vis.kanuri@gmail.com
R.
Suryanarayana
Department of Mathematics
Vishnu Institute of Technology
India
bhavyarsn@gmail.com
K. N.
Murty
Department of Applied Mathematics
Andhra University
India
nkanuri@hotmail.com
\(\Psi\)-bounded
\(\Psi\)-integrable
Lebesgue \(\Psi\)-delta integrable
Article.1.pdf
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G. F. Simmons, Introduction to Topology and Modern Analysis, Robert E. Krieger Publishing Co., Melbourne (2003)
]
Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems
Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems
en
en
Assume that \((W, g_{1,\infty})\) is a
nonautonomous discrete dynamical system given by sequences \((g_{m})_{m=1}^{\infty}\) of continuous maps on the space \((W,d)\).
In this paper, it is proven that if \(g_{1, \infty}\) is topologically weakly mixing and satisfies that
\(g_{1}^{n}\circ g_{1}^{m}=g_{1}^{n+m}\) for any \(n,m\in\{0,1,\ldots\}\), then it is distributional chaos in a sequence.
This result extends the existing one.
14
20
Yu
Zhao
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
datom@189.cn
Risong
Li
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
gdoulrs@163.com
Hongqing
Wang
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
wanghq3333@126.com
Haihua
Liang
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
lhhlucy@126.com
Chaotic in the sense of Devaney
topologically transitive
sensitive
nonautonomous discrete dynamical systems
distributional chaos in a sequence
Article.2.pdf
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]
Solution of Newell-Whitehead-Segel equation by variational iteration method with He's polynomials
Solution of Newell-Whitehead-Segel equation by variational iteration method with He's polynomials
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en
This article seeks to extend the variational iteration method (VIM) with He's polynomials for the approximate solution of nonlinear Newell-Whitehead-Segel equation (NWSE). Lagrange multiplier in correction functional is determined with the help of variational theory, and then homotopy perturbation method (HPM) is employed to dissolve the nonlinear terms. Thus a successful series is obtained with these iterations which are termed as He's polynomials. Result shows that this method is highly accurate and comes closer very quickly to the exact solution. We formulate three possible cases of NWSE to show the capability and ability of the present method. The valuable outcome discloses that the proposed strategy is very convenient, straightforward and can be utilized to linear and nonlinear problems.
21
29
Muhammad
Nadeem
School of Mathematical Sciences
Dalian University of Technology
China
Shao-Wen
Yao
School of Mathematics and Information Science
Henan Polytechnic University
China
yaoshaowen@hpu.edu.cn
Nusrat
Parveen
Department of Social Sciences
Govt. College University Faisalabad
Pakistan
NWSE
VIM
Lagrange multiplier
HPM
Article.3.pdf
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[1]
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H. K. Jassim, Homotopy perturbation algorithm using Laplace transform for Newell--Whitehead--Segel equation, Int. J. Adv. Appl. Math. Mech., 2 (2015), 8-12
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X.-X. Li, D. Tian, C.-H. He, J.-H. He, A fractal modification of the surface coverage model for an electrochemical arsenic sensor, Electrochimica Acta, 296 (2019), 491-493
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Z.-J. Liu, M. Y. Adamu, E. Suleiman, J.-H. He, Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations, Therm. Sci., 21 (2017), 1843-1846
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S. A. Manaa, An Approximate solution to the Newell--Whitehead--Segel equation by the Adomian decomposition method, Raf, J. Comput. Math., 8 (2011), 171-180
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M. Nadeem, F. Q. Li, Modified Laplace Variational Iteration Method for Analytical Approach of Klein--Gordon and Sine--Gordon Equations, Iran. J. Sci. Technol. Trans. A Sci., 43 (2018), 1933-1940
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M. Nadeem, F. Li, H. Ahmad, He's variational iteration method for solving non-homogeneous Cauchy Euler differential equations, Nonlinear Sci. Lett. A Math. Phys. Mech., 9 (2018), 231-237
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P. Pue-on, Laplace Adomian Decomposition Method for Solving Newell--Whitehead--Segel Equation, Appl. Math. Sci. (Ruse), 7 (2013), 6593-6600
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W. K. Zahra, W. A. Ouf, M. S. El-Azab, Cubic $B$-spline collocation algorithm for the numerical solution of Newell Whitehead Segel type equations, Electron. J. Math. Anal. Appl., 2 (2014), 81-100
]
A new quintic B-spline approximation for numerical treatment of Boussinesq equation
A new quintic B-spline approximation for numerical treatment of Boussinesq equation
en
en
In this work, we have presented a new quintic B-spline approximation technique for numerical solution of Boussinesq equation. Usual finite difference formulation has been applied to discretize the problem in temporal domain, whereas, the typical fifth degree B-spline functions, equipped with a new approximation for fourth order derivative, have been utilized to interpolate the unknown function in spatial direction. The stability and error analysis of the proposed numerical algorithm have been studied rigorously. Two test examples are considered to affirm the performance and accuracy of the new scheme. The computational outcomes are found to be better than the existing numerical techniques on the topic.
30
42
Tahir
Nazir
Department of Mathematics
University of Sargodha
Pakistan
Muhammad
Abbas
Department of Mathematics
University of Sargodha
Pakistan
muhammad.abbas@uos.edu.pk
Muhammad Kashif
Iqbal
Department of Mathematics
Government College University
Pakistan
Quintic B-spline functions
theta weighted scheme
quintic B-spline collocation method
Boussinesq equation
Von-Neumann stability
Article.4.pdf
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[1]
M. Abbas, M. K. Iqbal, B. Zafar, S. B. M. Zin, New cubic B-spline approximations for solving nonlinear Korteweg-de Vries equation, Indian J. Sci. Tech., 12 (2019), 1-9
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]
Analytical solution of the viscous flow over a stretching sheet by multi-step optimal homotopy asymptotic method
Analytical solution of the viscous flow over a stretching sheet by multi-step optimal homotopy asymptotic method
en
en
In this article the governing equations of viscous flow over a stretching sheet are reduced to ordinary boundary value problem by using a similarity transformation. The new analytical approach Multi-step Optimal Homotopy Asymptotic Method (MOHAM) is formulated and used for the boundary value problem. The numerical comparison of Homotopty Perturbation Method (HPM), exact solution, DTM, and numerical results (Runge Kutta Method) revealed that the new technique is powerful method for solving boundary layer equations. Also the solution is plotted for various values of \(\beta \).
43
49
M.
Fiza
Department of Mathematics
Abdul Wali Khan University
Pakistan
H.
Ullah
Department of Mathematics
Abdul Wali Khan University
Pakistan
hakeemullah1@gmail.com
S.
Islam
Department of Mathematics
Abdul Wali Khan University
Pakistan
F.
Chohan
Department of IT
Burraimi University College
Oman
MOHAM
boundary layer problem
Navier Stokes equations
DTM
Article.5.pdf
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S. Abbasbandy, A numerical solution of the Blasius equation by adomian's decomposition method and comparison with homotopy analysis method, Chaos Solitons Fractals, 31 (2007), 257-260
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A complementarity model and algorithm for supply chain with immediate marketing order
A complementarity model and algorithm for supply chain with immediate marketing order
en
en
Based on the research of supply chain management, a complementary model of supply chain with immediate marketing order single commodity is established. In order to give the optimal decision of the problem, a new-type algorithm is presented in this paper to obtain the solution of the model. The rationality of the model and the effectiveness of the algorithm are illustrated by an example.
50
57
Guirong
Pan
School of Information Science and Engineering
Linyi University
China
panguirong@lyu.edu.cn
Haodong
Chen
School of Mathematics and Statistics
Linyi University
China
2101058556@qq.com
Hongchun
Sun
School of Mathematics and Statistics
Linyi University
China
sunhongchun@sina.com
Immediate marketing
single commodity
complementarity model
algorithm
Article.6.pdf
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]
Note on the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners
Note on the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners
en
en
In this paper, we revisit the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners.
Our result essentially improves the corresponding result of Zhao et al. [L. Zhao, B. Qin, F. D. Chen, Adv. Difference Equ., \(\textbf{2018}\) (2018), 13 pages].
58
63
Runxin
Wu
School of Mathematics and Physics
Fujian University of Technology
China
18106069131@163.com
Lin
Li
School of Mathematics and Physics
Fujian University of Technology
China
Cooperative system
boundary equilibrium
global stability
Article.7.pdf
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Q. F. Lin, Allee effect increasing the final density of the species subject to the Allee effect in a Lotka Volterra commensal symbiosis model, Adv. Difference Equ., 2018 (2018), 1-9
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X. D. Xie, Y. L. Xue, R. X. Wu, Global attractivity in a discrete mutualism model with infinite deviating arguments, Discrete Dyn. Nat. Soc., 2017 (2017), 1-8
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Y. L. Xue, X. D. Xie, F. D. Chen, R. Y. Han, Almost periodic solution of a discrete commensalism system, Discrete Dyn. Nat. Soc., 2015 (2015), 1-11
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K. Yang, Z. S. Miao, F. D. Chen, X. D. Xie, Influence of single feedback control variable on an autonomous Holling II type cooperative system, J. Math. Anal. Appl., 435 (2016), 874-888
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K. Yang, X. D. Xie, F. D. Chen, Global stability of a discrete mutualism model, Abstr. Appl. Anal., 2014 (2014), 1-7
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L. Zhao, B. Qin, F. D. Chen, Permanence and global stability of a May cooperative system with strong and weak cooperative partners, Adv. Difference Equ., 2018 (2018), 1-13
]
Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers
Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers
en
en
In this paper, we investigate the invertibility of \(n\times n\) skew circulant matrix involving the product of Fibonacci and Lucas numbers, whose determinant and inverse can be expressed by the \((n-1)^{\rm th}\), \(n^{\rm th}\), \((n+1)^{\rm th}\), \((n+2)^{\rm th}\) product of Fibonacci and Lucas numbers. Some norms and bounds for the spread of these matrices are given, respectively. In addition, we generalize these results to skew left circulant matrix involving the product of Fibonacci and Lucas numbers. Finally, several numerical examples are illustrated to show the effectiveness of our theoretical results.
64
78
Yunlan
Wei
School of Mathematics and Statistics
College of Information Technology
Linyi University
The University of Suwon
China
Korea
Yanpeng
Zheng
School of Automation and Electrical Engineering
Linyi University
China
zhengyanpeng0702@sina.com
Zhaolin
Jiang
School of Mathematics and Statistics
Linyi University
China
jzh1208@sina.com
Sugoog
Shon
College of Information Technology
The University of Suwon
Korea
Determinant
inverse
norm
spread
Fibonacci number
skew circulant matrix
Article.8.pdf
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]