Solving multi-order fractional differential equations by reproducing kernel Hilbert space method
Reza
Khoshsiar Ghaziani
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
author
Mojtaba
Fardi
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
author
Mehdi
Ghasemi
Department of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
3
no.
2016
170
190
http://cmde.tabrizu.ac.ir/article_5569_189468c3c1cfa4d5821a091910f3c06f.pdf
Application of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation
K. R.
Raslan
Mathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City (11884), Cairo, Egypt
author
Talaat
S. EL-Danaf
Mathematics Department, Faculty of Science,
Menoufia University, Shebein El-Koom, Egypt
author
khalid
k. Ali
Mathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City (11884), Cairo, Egypt
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
3
no.
2016
191
204
http://cmde.tabrizu.ac.ir/article_5570_86ab1d2e732c832d0de3415cce6904ef.pdf
Superconvergence analysis of multistep collocation method for delay functional integral equations
Parviz
Darania
Department of Mathematics, Faculty of Science,
Urmia University, P.O.Box 165, Urmia-Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
3
no.
2016
205
216
http://cmde.tabrizu.ac.ir/article_5575_ecd71d3064d3f8d769052f60133fab2e.pdf
A hybrid method with optimal stability properties for the numerical solution of stiff differential systems
Akram
Movahedinejad
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
author
Ali
Abdi
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
author
Gholamreza
Hojjati
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
3
no.
2016
217
229
http://cmde.tabrizu.ac.ir/article_5577_9a6e6267bbdc1501201d589bb27346de.pdf
Numerical method for solving optimal control problem of the linear differential systems with inequality constraints
Farshid
Mirzaee
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
author
Afsun
Hamzeh
Faculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
3
no.
2016
230
248
http://cmde.tabrizu.ac.ir/article_5578_529738c257731433a12017966bed9308.pdf
Numerical solution of variational problems via Haar wavelet quasilinearization technique
Mohammad
Zarebnia
Department of Mathematics,
University of Mohaghegh Ardabili,
56199-11367 Ardabil, Iran
author
Hosein
Barandak Emcheh
Department of Mathematics,
University of Mohaghegh Ardabili,
56199-11367 Ardabil, Iran
author
text
article
2016
eng
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.
Computational Methods for Differential Equations
University of Tabriz
2345-3982
4
v.
3
no.
2016
249
260
http://cmde.tabrizu.ac.ir/article_5586_74fa28052edadac180c8a9c7f53a8351.pdf