2016
4
3
3
91
Solving multiorder fractional differential equations by reproducing kernel Hilbert space method
2
2
In this paper we propose a relatively new semianalytical technique to approximate the solution of nonlinear multiorder fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multiorder FDEs and discuss the existence of solution for nonlinear multiorder FDEs in reproducing kernel Hilbert space (RKHS). We further give an error analysis for the proposed technique in different reproducing kernel Hilbert spaces and present some useful results. The accuracy of the proposed technique is examined by comparing with the exact solution of some test examples.
1

170
190


Reza
Khoshsiar Ghaziani
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
Department of Applied Mathematics, Faculty
I. R. Iran
rkhoshsiar@gmail.com


Mojtaba
Fardi
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
Department of Applied Mathematics, Faculty
I. R. Iran
fardi_mojtaba@yahoo.com


Mehdi
Ghasemi
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
Department of Applied Mathematics, Faculty
I. R. Iran
meh_ghasemi@yahoo.com
MultiOrder Fractional
Hilbert space
Reproducing kernel method
Error analysis
Application of linear combination between cubic Bspline collocation methods with different basis for solving the KdV equation
2
2
In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using a new approach by combining cubic Bspline functions. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using vonNeumann technique. To test accuracy the error norms L2, L∞ are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.
1

191
204


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


Talaat
S. ELDanaf
Mathematics Department, Faculty of Science,
Menoufia University, Shebein ElKoom, Egypt
Mathematics Department, Faculty of Science,
Menouf
Egypt
talaat11@yahoo.com


khalid
k. Ali
Mathematics Department, Faculty of Science,
AlAzhar University, NasrCity (11884), Cairo, Egypt
Mathematics Department, Faculty of Science,
AlAzh
Egypt
khalidkaram2012@yahoo.com
Collocation method
cubic BSpline methods
KdV equation
Superconvergence analysis of multistep collocation method for delay functional integral equations
2
2
In this paper, we will present a review of the multistep collocation method for Delay Volterra Integral Equations (DVIEs) from [1] and then, we study the superconvergence analysis of the multistep collocation method for DVIEs. Some numerical examples are given to confirm our theoretical results.
1

205
216


Parviz
Darania
Department of Mathematics, Faculty of Science,
Urmia University, P.O.Box 165, UrmiaIran
Department of Mathematics, Faculty of Science,
Urm
I. R. Iran
p.darania@urmia.ac.ir
Delay integral equations
Multistep collocation method
Convergence and superconvergence
A hybrid method with optimal stability properties for the numerical solution of stiff differential systems
2
2
In this paper, we consider the construction of a new class of numerical methods based on the backward differentiation formulas (BDFs) that be equipped by including two offstep points. We represent these methods from general linear methods (GLMs) point of view which provides an easy process to improve their stability properties and implementation in a variable stepsize mode. These superiorities are confirmed by the numerical examples.
1

217
229


Akram
Movahedinejad
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences,
University
I. R. Iran
a_movahedinejad@tabrizu.ac.ir


Ali
Abdi
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences,
University
I. R. Iran
a_abdi@tabrizu.ac.ir


Gholamreza
Hojjati
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences,
University
I. R. Iran
ghojjati@tabrizu.ac.ir
Backward differentiation formula
Hybrid methods
General linear methods
$A$ and $A(alpha)$stability
Variable stepsize implementation
Numerical method for solving optimal control problem of the linear differential systems with inequality constraints
2
2
In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the order of convergence is O(h4). Finally, numerical examples affirm the efficiency of the proposed method.
1

230
248


Farshid
Mirzaee
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 6571995863, Malayer, Iran
Faculty of Mathematical Sciences and Statistics,
M
I. R. Iran
f.mirzaee@malayeru.ac.ir


Afsun
Hamzeh
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 6571995863, Malayer, Iran
Faculty of Mathematical Sciences and Statistics,
M
I. R. Iran
afsoon.hamzeh@gmail.com
Adjustment of hat basis functions
Optimal control
Differential systems
Inequality constraint
Error analysis
Numerical solution of variational problems via Haar wavelet quasilinearization technique
2
2
In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear EulerLagrange equations which arise from the problems in calculus of variations. Some examples of variational problems are given and outcomes compared with exact solutions to demonstrate the accuracy and efficiency of the method.
1

249
260


Mohammad
Zarebnia
Department of Mathematics,
University of Mohaghegh Ardabili,
5619911367 Ardabil, Iran
Department of Mathematics,
University of
I. R. Iran
zarebnia@uma.ac.ir


Hosein
Barandak Emcheh
Department of Mathematics,
University of Mohaghegh Ardabili,
5619911367 Ardabil, Iran
Department of Mathematics,
University of
I. R. Iran
barhosein@gmail.com
Calculus of variation
Boundary value problem
Haar wavelet
Quasilinearization