University of TabrizComputational Methods for Differential Equations2345-39824320160701Solving multi-order fractional differential equations by reproducing kernel Hilbert space method1701905569ENRezaKhoshsiar GhazianiDepartment of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, IranMojtabaFardiDepartment of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, IranMehdiGhasemiDepartment of Applied Mathematics, Faculty of Mathematical Science,
Shahrekord University, Shahrekord, P. O. Box 115, IranJournal Article20161011In 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.https://cmde.tabrizu.ac.ir/article_5569_189468c3c1cfa4d5821a091910f3c06f.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39824320160701Application of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation1912045570ENK. R.RaslanMathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City (11884), Cairo, EgyptTalaatS. EL-DanafMathematics Department, Faculty of Science,
Menoufia University, Shebein El-Koom, EgyptKhalidK. AliMathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City (11884), Cairo, EgyptJournal Article20160823In 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.https://cmde.tabrizu.ac.ir/article_5570_86ab1d2e732c832d0de3415cce6904ef.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39824320160701Superconvergence analysis of multistep collocation method for delay functional integral equations2052165575ENParvizDaraniaDepartment of Mathematics, Faculty of Science,
Urmia University, P.O.Box 165, Urmia-IranJournal Article20160620In this paper, we will present a review of the multistep collocation method for Delay Volterra Integral Equations (DVIEs) from <br />[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.https://cmde.tabrizu.ac.ir/article_5575_ecd71d3064d3f8d769052f60133fab2e.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39824320160701A hybrid method with optimal stability properties for the numerical solution of stiff differential systems2172295577ENAkramMovahedinejadFaculty of Mathematical Sciences,
University of Tabriz, Tabriz, IranAliAbdiFaculty of Mathematical Sciences,
University of Tabriz, Tabriz, IranGholamrezaHojjatiFaculty of Mathematical Sciences,
University of Tabriz, Tabriz, Iran0000-0001-8406-763XJournal Article20161123In 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.https://cmde.tabrizu.ac.ir/article_5577_9a6e6267bbdc1501201d589bb27346de.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39824320160701Numerical method for solving optimal control problem of the linear differential systems with inequality constraints2302485578ENFarshidMirzaeeFaculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, Iran0000-0002-1429-2548AfsunHamzehFaculty of Mathematical Sciences and Statistics,
Malayer University, P. O. Box 65719-95863, Malayer, IranJournal Article20161025In 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.https://cmde.tabrizu.ac.ir/article_5578_529738c257731433a12017966bed9308.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39824320160701Numerical solution of variational problems via Haar wavelet quasilinearization technique2492605586ENMohammadZarebniaDepartment of Mathematics,
University of Mohaghegh Ardabili,
56199-11367 Ardabil, IranHoseinBarandak EmchehDepartment of Mathematics,
University of Mohaghegh Ardabili,
56199-11367 Ardabil, IranJournal Article20160709In 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.https://cmde.tabrizu.ac.ir/article_5586_74fa28052edadac180c8a9c7f53a8351.pdf