2015
3
3
3
84
Solving highorder partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
2
2
In this paper, a collocation method for solving highorder linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of derivatives. All principles and properties of the ESC functions are derived and introduced by us as a new basis defined in the whole range. The method transforms the PDEs and conditions into block matrix equations, which correspond to system of linear algebraic equations with unknown ESC coefficients, by using ESC collocation points. Combining these matrix equations and then solving the system yield the ESC coefficients of the solution function. Numerical examples are included to test the validity and applicability of the method.
1

147
162


Mohamed AbdelLatif
Ramadan
Mathematics Department, Faculty of Science, Menoufia University, Shebein ElKoom, Egypt
Mathematics Department, Faculty of Science,
Egypt
ramadanmohamed13@yahoo.com


Kamal Mohamed
Raslsn
Mathematics Department, Faculty of Science, AlAzhar University, NasrCity, Cairo, Egypt
Mathematics Department, Faculty of Science,
Egypt
kamal_raslan@yahoo.com


Talaat ElSayed
ElDanaf
Department of Mathematics and Statistics, Taibah University Madinah Munawwarah, KSA
Department of Mathematics and Statistics,
Saudi Arabia
talaat11@yahoo.com


Mohamed
Abd El Salam
Mathematics Department, Faculty of Science
AlAzhar University, NasrCity, 11884, Cairo, Egypt
Mathematics Department, Faculty of Science
Egypt
mohamed_salam1985@yahoo.com
Exponential second kind Chebyshev functions
Highorder partial differential equations
Collocation method
Iterative scheme to a coupled system of highly nonlinear fractional order differential equations
2
2
In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of the method. We provide an example to illustrate our main results.
1

163
176


Kamal
Shah
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of
Pakistan
kamalshah408@gmail.com


Rahmat
Khan
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, University of
Pakistan
rahmat_alipk@yahoo.com
Coupled system
Mixed type boundary conditions, Upper and lower solutions, Monotone iterative technique, Existence and uniqueness results
Solution of BangBang Optimal Control Problems by Using Bezier Polynomials
2
2
In this paper, a new numerical method is presented for solving the optimal control problems of BangBang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and conditions. Illustrative examples are included to demonstrate the validity and applicability of the method.
1

177
191


Ayatollah
Yari
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
Payame Noor University, PO BOX 193953697, Tehran, Iran
Department of Applied Mathematics,
Faculty
I. R. Iran
a_yary@yahoo.com


Mirkamal
Mirnia
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz
Department of Applied Mathematics,
Faculty
I. R. Iran
mirniakam@tabrizu.ac.ir


Aghileh
Heydari
Department of Applied Mathematics,
Faculty of Mathematical Sciences,
Payame Noor University, PO BOX 193953697, Tehran,Iran
Department of Applied Mathematics,
Faculty
I. R. Iran
a_heidari@pnu.ac.ir
Optimal control
BangBang control
Minimumtime
Bezier polynomials family
Best approximation
Explicit exact solutions for variable coefficient BroerKaup equations
2
2
Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, solitonlike, periodic and rational solutions are obtained for (2+1)dimensional variable coefficient BroerKaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient BroerKaup system.
1

192
199


Manjit
Singh
Yadawindra College of Engineering
Punjabi University Guru Kashi Campus
Talwandi Sabo151302, Punjab, India
Yadawindra College of Engineering
Punjabi
India
manjitcsir@gmail.com


R.K.
Gupta
Centre for Mathematics and Statistics
School of Basic and Applied Sciences, Central University of Punjab,
Bathinda151001, Punjab, India
Centre for Mathematics and Statistics
School
India
rajeshgupt@thapar.edu
BroerKaup equations
Riccati equation mapping method
Explicit exact solutions
An application of differential transform method for solving nonlinear optimal control problems
2
2
In this paper, we present a capable algorithm for solving a class of nonlinear optimal control problems (OCP's). The approach rest mainly on the differential transform method (DTM) which is one of the approximate methods. The DTM is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. Utilizing this approach, the optimal control and the corresponding trajectory of the OCP's are found in the form of rapidly convergent series with easily computed components. Numerical results are also given for several test examples to demonstrate the applicability and the efficiency of the method.
1

200
217


Alireza
Nazemi
Department of Mathematics,
School of Mathematical Sciences,
Shahrood University of Technology,
P.O. Box 3619995161316, TelFax No:+98 2332300235,
Shahrood, Iran
Department of Mathematics,
School of Mathematical
I. R. Iran
nazemi20042003@gmail.com


Saiedeh
Hesam
Department of Mathematics,
School of Mathematical Sciences,
Shahrood University of Technology,
P.O. Box 3619995161316, TelFax No:+98 2332300235,
Shahrood, Iran
Department of Mathematics,
School of Mathematical
I. R. Iran
taranome2009@yahoo.com


Ahmad
Haghbin
Department of Mathematics, Gorgan branch,
Islamic Azad University, Gorgan, Iran
Department of Mathematics, Gorgan branch,
Islamic
I. R. Iran
ahmadbin@yahoo.com
Optimal Control Problems
Differential transform method
Hamiltonian system
Nonpolynomial Spline Method for Solving Coupled Burgers Equations
2
2
In this paper, nonpolynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using VonNeumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations. These results show that the technique introduced here is accurate and easy to apply.
1

218
230


Khalid
K. Ali
Department, Faculty of Science,
AlAzhar University, Nasr City (11884), Cairo, Egypt
Department, Faculty of Science,
AlAzhar
Egypt
khalidkaram2012@yahoo.com


K. R.
Raslan
Department, Faculty of Science,
AlAzhar University, Nasr City (11884), Cairo, Egypt.
Department, Faculty of Science,
AlAzhar
Egypt
kamal_raslan@yahoo.com


Talaat S.
ElDanaf
Mathematics Department, Faculty of Science, Menoufia University, Shebein ElKoom, Egypt
Mathematics Department, Faculty of Science,
Saudi Arabia
talaat11@yahoo.com
Nonpolynomial
spline method
Coupled
Burger’s
Equations