University of Tabriz Computational Methods for Differential Equations 2345-3982 3 4 2015 10 01 A new iteration method for solving a class of Hammerstein type integral equations system 231 246 4975 EN Saeed Karimi Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran Maryam Dehghan Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran Fariba Takhtabnoos Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran Journal Article 2016 06 10 In 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.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 3 4 2015 10 01 Numerical solution of Troesch's problem using Christov rational functions 247 257 5003 EN Abbas Saadatmandi Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran Tahereh Abdolahi-Niasar Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran Journal Article 2016 07 24 We 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.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 3 4 2015 10 01 Solving large systems arising from fractional models by preconditioned methods 258 273 5427 EN Reza Khoshsiar Ghaziani Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran Mojtaba Fardi Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran Mehdi Ghasemi Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran Journal Article 2015 10 01 This 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.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 3 4 2015 10 01 Finite-time stabilization of satellite quaternion attitude 274 283 5431 EN Mohammad Reza Niknam Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran Aghileh Heydari Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran Journal Article 2016 09 20 In 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.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 3 4 2015 10 01 A rational Chebyshev functions approach for Fredholm-Volterra integro-differential equations 284 297 5430 EN Mohamed Abdel-Latif Ramadan Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Kom, Egypt Kamal. Mohamed Raslan Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt Mahmoud Abd El Ghanny Nassear Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt Journal Article 2016 08 24 The 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.pdf
University of Tabriz Computational Methods for Differential Equations 2345-3982 3 4 2015 10 01 Valuation of installment option by penalty method 298 310 5005 EN Ali Beiranvand Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Karim Ivaz Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Journal Article 2016 06 28 In 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