University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
3
2016
07
01
Solving multi-order fractional differential equations by reproducing kernel Hilbert space method
170
190
EN
Reza
Khoshsiar Ghaziani
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
rkhoshsiar@gmail.com
Mojtaba
Fardi
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
fardi_mojtaba@yahoo.com
Mehdi
Ghasemi
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
meh_ghasemi@yahoo.com
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.
Multi-Order Fractional,Hilbert space,Reproducing kernel method,Error analysis
http://cmde.tabrizu.ac.ir/article_5569.html
http://cmde.tabrizu.ac.ir/article_5569_189468c3c1cfa4d5821a091910f3c06f.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
3
2016
07
01
Application of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation
191
204
EN
K. R.
Raslan
Mathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City (11884), Cairo, Egypt
kamal_raslan@yahoo.com
Talaat
S. EL-Danaf
Mathematics Department, Faculty of Science,
Menoufia University, Shebein El-Koom, Egypt
talaat11@yahoo.com
khalid
k. Ali
Mathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City (11884), Cairo, Egypt
khalidkaram2012@yahoo.com
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.
Collocation method,cubic B-Spline methods,KdV equation
http://cmde.tabrizu.ac.ir/article_5570.html
http://cmde.tabrizu.ac.ir/article_5570_86ab1d2e732c832d0de3415cce6904ef.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
3
2016
07
01
Superconvergence analysis of multistep collocation method for delay functional integral equations
205
216
EN
Parviz
Darania
Department of Mathematics, Faculty of Science,
Urmia University, P.O.Box 165, Urmia-Iran
p.darania@urmia.ac.ir
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.
Delay integral equations,Multistep collocation method,Convergence and superconvergence
http://cmde.tabrizu.ac.ir/article_5575.html
http://cmde.tabrizu.ac.ir/article_5575_ecd71d3064d3f8d769052f60133fab2e.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
3
2016
07
01
A hybrid method with optimal stability properties for the numerical solution of stiff differential systems
217
229
EN
Akram
Movahedinejad
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
a_movahedinejad@tabrizu.ac.ir
Ali
Abdi
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
a_abdi@tabrizu.ac.ir
Gholamreza
Hojjati
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
ghojjati@tabrizu.ac.ir
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.
Backward differentiation formula,Hybrid methods,General linear methods,$A$-- and $A(alpha)$--stability,Variable stepsize implementation
http://cmde.tabrizu.ac.ir/article_5577.html
http://cmde.tabrizu.ac.ir/article_5577_9a6e6267bbdc1501201d589bb27346de.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
3
2016
07
01
Numerical method for solving optimal control problem of the linear differential systems with inequality constraints
230
248
EN
Farshid
Mirzaee
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
f.mirzaee@malayeru.ac.ir
Afsun
Hamzeh
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
afsoon.hamzeh@gmail.com
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.
Adjustment of hat basis functions,Optimal control,Differential systems,Inequality constraint,Error analysis
http://cmde.tabrizu.ac.ir/article_5578.html
http://cmde.tabrizu.ac.ir/article_5578_529738c257731433a12017966bed9308.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
4
3
2016
07
01
Numerical solution of variational problems via Haar wavelet quasilinearization technique
249
260
EN
Mohammad
Zarebnia
Department of Mathematics,
University of Mohaghegh Ardabili,
56199-11367 Ardabil, Iran
zarebnia@uma.ac.ir
Hosein
Barandak Emcheh
Department of Mathematics,
University of Mohaghegh Ardabili,
56199-11367 Ardabil, Iran
barhosein@gmail.com
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.
Calculus of variation,Boundary value problem,Haar wavelet,Quasilinearization
http://cmde.tabrizu.ac.ir/article_5586.html
http://cmde.tabrizu.ac.ir/article_5586_74fa28052edadac180c8a9c7f53a8351.pdf