eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-10-01
3
4
231
246
4975
A new iteration method for solving a class of Hammerstein type integral equations system
Saeed Karimi
karimijafarbigloo@gmail.com
1
Maryam Dehghan
maryamdehghan880@yahoo.com
2
Fariba Takhtabnoos
f.takhtabnoos@sutech.ac.ir
3
Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran
Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran
Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran
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.
http://cmde.tabrizu.ac.ir/article_4975_4e7277dbaf573b77ca57f7b2f6d7b882.pdf
Iterative method
Nonlinear integral equations system
Hammerstein integral equation
Fixed point iteration
Contraction operator
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-10-01
3
4
247
257
5003
Numerical solution of Troesch's problem using Christov rational functions
Abbas Saadatmandi
a.saadatmandi@gmail.com
1
Tahereh Abdolahi-Niasar
abdolahi.tahereh@yahoo.com
2
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran
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.
http://cmde.tabrizu.ac.ir/article_5003_aaa09fae46465928c72b2411e693a1d4.pdf
Troesch's problem
Christov functions
Collocation
Wiener functions
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-10-01
3
4
258
273
5427
Solving large systems arising from fractional models by preconditioned methods
Reza Khoshsiar Ghaziani
rkhoshsiar@gmail.com
1
Mojtaba Fardi
fardi_mojtaba@yahoo.com
2
Mehdi Ghasemi
m_ghasemi@yahoo.com
3
Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
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.
http://cmde.tabrizu.ac.ir/article_5427_0c086889fda355db3a47f172f6d03568.pdf
Krylov subspace methods
. Preconditioning techniques
Fractional model
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-10-01
3
4
274
283
5431
Finite-time stabilization of satellite quaternion attitude
Mohammad Reza Niknam
rezanik82@yahoo.com
1
Aghileh Heydari
a_heidari@pnu.ac.ir
2
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran
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.
http://cmde.tabrizu.ac.ir/article_5431_a252cee90ea89b91d31541dff4061ba8.pdf
Finite-time stabilization
quaternion
satellite attitude
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-10-01
3
4
284
297
5430
A rational Chebyshev functions approach for Fredholm-Volterra integro-differential equations
Mohamed Abdel-Latif Ramadan
ramadanmohamed13@yahoo.com
1
Kamal. Mohamed Raslan
kamal_raslan@yahoo.com
2
Mahmoud Abd El Ghanny Nassear
m7moudscience@yahoo.com
3
Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Kom, Egypt
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
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.
http://cmde.tabrizu.ac.ir/article_5430_288edd08b120ededf342db7e75540a7b.pdf
Rational Chebyshev functions
Fredholm-Volterra integro-differential equations
Collocation method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-10-01
3
4
298
310
5005
Valuation of installment option by penalty method
Ali Beiranvand
alibeiranvand36@gmail.com
1
Karim Ivaz
ivaz@tabrizu.ac.ir
2
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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.
http://cmde.tabrizu.ac.ir/article_5005_63ae507b538b5501876dab8b92feb175.pdf
Installment option
Black-Scholes model
penalty method
Free boundary problem