2018-08-17T19:17:10Z
http://cmde.tabrizu.ac.ir/?_action=export&rf=summon&issue=824
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2016
4
3
Solving multi-order fractional differential equations by reproducing kernel Hilbert space method
Reza
Khoshsiar Ghaziani
Mojtaba
Fardi
Mehdi
Ghasemi
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
2016
07
01
170
190
http://cmde.tabrizu.ac.ir/article_5569_189468c3c1cfa4d5821a091910f3c06f.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2016
4
3
Application of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation
K. R.
Raslan
Talaat
S. EL-Danaf
khalid
k. Ali
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
2016
07
01
191
204
http://cmde.tabrizu.ac.ir/article_5570_86ab1d2e732c832d0de3415cce6904ef.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2016
4
3
Superconvergence analysis of multistep collocation method for delay functional integral equations
Parviz
Darania
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
2016
07
01
205
216
http://cmde.tabrizu.ac.ir/article_5575_ecd71d3064d3f8d769052f60133fab2e.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2016
4
3
A hybrid method with optimal stability properties for the numerical solution of stiff differential systems
Akram
Movahedinejad
Ali
Abdi
Gholamreza
Hojjati
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
2016
07
01
217
229
http://cmde.tabrizu.ac.ir/article_5577_9a6e6267bbdc1501201d589bb27346de.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2016
4
3
Numerical method for solving optimal control problem of the linear differential systems with inequality constraints
Farshid
Mirzaee
Afsun
Hamzeh
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
2016
07
01
230
248
http://cmde.tabrizu.ac.ir/article_5578_529738c257731433a12017966bed9308.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2016
4
3
Numerical solution of variational problems via Haar wavelet quasilinearization technique
Mohammad
Zarebnia
Hosein
Barandak Emcheh
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
2016
07
01
249
260
http://cmde.tabrizu.ac.ir/article_5586_74fa28052edadac180c8a9c7f53a8351.pdf