University of TabrizComputational Methods for Differential Equations2345-39823420151001A new iteration method for solving a class of Hammerstein type integral equations system2312464975ENSaeedKarimiDepartment of Mathematics,
Persian Gulf University,
Bushehr 75169, IranMaryamDehghanDepartment of Mathematics,
Persian Gulf University,
Bushehr 75169, IranFaribaTakhtabnoosDepartment of Mathematics,
Persian Gulf University,
Bushehr 75169, IranJournal Article20160610In this work, a new iterative method is proposed for obtaining the approximate solution of a class of Hammerstein type Integral Equations System. The main structure of this method is based on the Richardson iterative method for solving an algebraic linear system of equations. Some conditions for existence and unique solution of this type equations are imposed. Convergence analysis and error bound estimation of the new iterative method are also discussed. Finally, some numerical examples are given to compare the performance of the proposed method with the existing methods.https://cmde.tabrizu.ac.ir/article_4975_4e7277dbaf573b77ca57f7b2f6d7b882.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823420151001Numerical solution of Troesch's problem using Christov rational functions2472575003ENAbbasSaadatmandiDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Kashan, Kashan 87317-53153, Iran0000-0002-7744-7770TaherehAbdolahi-NiasarDepartment of Applied Mathematics,
Faculty of Mathematical Sciences,
University of Kashan, Kashan 87317-53153, IranJournal Article20160724We present a collocation method to obtain the approximate solution of Troesch's problem which arises in the confinement of a plasma column by radiation pressure and applied physics. By using the Christov rational functions and collocation points, this method transforms Troesch's problem into a system of nonlinear algebraic equations. The rate of convergence is shown to be exponential. The numerical results obtained by the present method compares favorably with those obtained by various methods earlier in the literature.https://cmde.tabrizu.ac.ir/article_5003_aaa09fae46465928c72b2411e693a1d4.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823420151001Solving large systems arising from fractional models by preconditioned methods2582735427ENRezaKhoshsiar GhazianiFaculty of Mathematical Sciences,
Shahrekord University,
P. O. Box 115, Shahrekord, IranMojtabaFardiFaculty of Mathematical Sciences,
Shahrekord University,
P. O. Box 115, Shahrekord, IranMehdiGhasemiFaculty of Mathematical Sciences,
Shahrekord University,
P. O. Box 115, Shahrekord, IranJournal Article20151001This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient for normal residual( preconditioned CGN) method, to solve the corresponding discritized systems. We further make comparisons between the preconditioners commonly used in the parallelization of the preconditioned Krylov subspace methods. The results suggest that preconditioning technique is a promising candidate for solving large-scale linear systems arising from fractional models.https://cmde.tabrizu.ac.ir/article_5427_0c086889fda355db3a47f172f6d03568.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823420151001Finite-time stabilization of satellite quaternion attitude2742835431ENMohammad RezaNiknamDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, IranAghilehHeydariDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, IranJournal Article20160920In this paper, a finite-time control scheme is presented for stabilization of the satellite chaotic attitude around its equilibrium point when its attitude is confused by a disturbed torque. Controllers and settling time of stabilizaton are obtained, based on the Lyapunov stability theorem and finite-time control scheme. This method is satisfied for any initial condition. Numerical simulations are presented to illustrate the ability and effectiveness of proposed method. https://cmde.tabrizu.ac.ir/article_5431_a252cee90ea89b91d31541dff4061ba8.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823420151001A rational Chebyshev functions approach for Fredholm-Volterra integro-differential equations2842975430ENMohamedAbdel-Latif RamadanMathematics Department, Faculty of Science,
Menoufia University, Shebein El-Kom, EgyptKamal. MohamedRaslanMathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City, Cairo, EgyptMahmoud Abd El GhannyNassearMathematics Department, Faculty of Science,
Al-Azhar University, Nasr-City, Cairo, EgyptJournal Article20160824The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The proposed method is numerically compared with others existing methods where it maintains better accuracy.https://cmde.tabrizu.ac.ir/article_5430_288edd08b120ededf342db7e75540a7b.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823420151001Valuation of installment option by penalty method2983105005ENAliBeiranvandFaculty of Mathematical Sciences,
University of Tabriz, Tabriz, IranKarimIvazFaculty of Mathematical Sciences,
University of Tabriz, Tabriz, IranJournal Article20160628In this paper, installment options on the underlying asset which evolves according to Black-Scholes model and pays constant dividend to its owner will be considered. Applying arbitrage pricing theory, the non-homogeneous parabolic partial differential equation governing the value of installment option is derived. Then, penalty method is used to value the European continuous installment call option.https://cmde.tabrizu.ac.ir/article_5005_63ae507b538b5501876dab8b92feb175.pdf