eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-07-01
4
3
170
190
5569
Solving multi-order fractional differential equations by reproducing kernel Hilbert space method
Reza Khoshsiar Ghaziani
rkhoshsiar@gmail.com
1
Mojtaba Fardi
fardi_mojtaba@yahoo.com
2
Mehdi Ghasemi
meh_ghasemi@yahoo.com
3
Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran
Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran
Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran
In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order 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.
http://cmde.tabrizu.ac.ir/article_5569_189468c3c1cfa4d5821a091910f3c06f.pdf
Multi-Order Fractional
Hilbert space
Reproducing kernel method
Error analysis
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-07-01
4
3
191
204
5570
Application of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation
K. R. Raslan
kamal_raslan@yahoo.com
1
Talaat S. EL-Danaf
talaat11@yahoo.com
2
khalid k. Ali
khalidkaram2012@yahoo.com
3
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City (11884), Cairo, Egypt
Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City (11884), Cairo, Egypt
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 B-spline functions. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann 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.
http://cmde.tabrizu.ac.ir/article_5570_86ab1d2e732c832d0de3415cce6904ef.pdf
Collocation method
cubic B-Spline methods
KdV equation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-07-01
4
3
205
216
5575
Superconvergence analysis of multistep collocation method for delay functional integral equations
Parviz Darania
p.darania@urmia.ac.ir
1
Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 165, Urmia-Iran
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.
http://cmde.tabrizu.ac.ir/article_5575_ecd71d3064d3f8d769052f60133fab2e.pdf
Delay integral equations
Multistep collocation method
Convergence and superconvergence
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-07-01
4
3
217
229
5577
A hybrid method with optimal stability properties for the numerical solution of stiff differential systems
Akram Movahedinejad
a_movahedinejad@tabrizu.ac.ir
1
Ali Abdi
a_abdi@tabrizu.ac.ir
2
Gholamreza Hojjati
ghojjati@tabrizu.ac.ir
3
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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 off--step 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.
http://cmde.tabrizu.ac.ir/article_5577_9a6e6267bbdc1501201d589bb27346de.pdf
Backward differentiation formula
Hybrid methods
General linear methods
$A$-- and $A(alpha)$--stability
Variable stepsize implementation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-07-01
4
3
230
248
5578
Numerical method for solving optimal control problem of the linear differential systems with inequality constraints
Farshid Mirzaee
f.mirzaee@malayeru.ac.ir
1
Afsun Hamzeh
afsoon.hamzeh@gmail.com
2
Faculty of Mathematical Sciences and Statistics, Malayer University, P. O. Box 65719-95863, Malayer, Iran
Faculty of Mathematical Sciences and Statistics, Malayer University, P. O. Box 65719-95863, Malayer, Iran
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.
http://cmde.tabrizu.ac.ir/article_5578_529738c257731433a12017966bed9308.pdf
Adjustment of hat basis functions
Optimal control
Differential systems
Inequality constraint
Error analysis
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2016-07-01
4
3
249
260
5586
Numerical solution of variational problems via Haar wavelet quasilinearization technique
Mohammad Zarebnia
zarebnia@uma.ac.ir
1
Hosein Barandak Emcheh
barhosein@gmail.com
2
Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran
Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran
In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear Euler-Lagrange 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.
http://cmde.tabrizu.ac.ir/article_5586_74fa28052edadac180c8a9c7f53a8351.pdf
Calculus of variation
Boundary value problem
Haar wavelet
Quasilinearization