University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 1 Issue 1 2013 05 01 A new model of (I+S)-type preconditioner for system of linear equations 1 14 EN Hashem Saberi Najafi hnajafi@guilan.ac.ir Seyyed Ahmad Edalatpanah saedalatpanah@gmail.com Amir Hossein Refahi Sheikhani ah_refahi@yahoo.com In this paper, we design a new model of preconditioner for systems of linear equations. The convergence properties of the proposed methods have been analyzed and compared with the classical methods. Numerical experiments of convection-diffusion equations show a good im- provement on the convergence, and show that the convergence rates of proposed methods are superior to the other modified iterative methods. https://jmm.guilan.ac.ir/article_93.html https://jmm.guilan.ac.ir/article_93_b4db128b77ca7337ef098743583ad747.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 1 Issue 1 2013 05 01 Global conjugate gradient method for solving large general Sylvester matrix equation 15 27 EN Saeed Karimi karimi@pgu.ac.ir In this paper, an iterative method is proposed for solving large general Sylvester matrix equation \$AXB+CXD = E\$, where \$A in R^{ntimes n}\$ , \$C in R^{ntimes n}\$ , \$B in R^{stimes s}\$ and  \$D in R^{stimes s}\$ are given matrices and \$X in R^{stimes s}\$  is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-hand sides. By defining a linear matrix operator and imposing some conditions on this operator, we demonstrate how to employ the GL-CG algorithm for solving large general Sylvester matrix equation. Finally, some numerical experi- ments are given to illustrate the efficiency of the method. https://jmm.guilan.ac.ir/article_94.html https://jmm.guilan.ac.ir/article_94_1e1d28447d734ae7d2d734743b7e1042.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 1 Issue 1 2013 05 01 Solving a class of nonlinear two-dimensional Volterra integral equations by using two-dimensional triangular orthogonal functions 28 40 EN Farshid Mirzaee f.mirzaee@malayeru.ac.ir In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods. https://jmm.guilan.ac.ir/article_95.html https://jmm.guilan.ac.ir/article_95_1fd90cc636e55d438249335afa4f5fa4.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 1 Issue 1 2013 05 01 Application of Laplace decomposition method for Burgers-Huxley and Burgers-Fisher equations 41 67 EN Mohammad Reza Yaghouti yaghouti@guilan.ac.ir Ali Zabihi alizabihi90@yahoo.com In this paper, we apply the Laplace decomposition method to obtain a series solutions of the Burgers-Huxley and Burgers-Fisher equations. The technique is based on the application of Laplace transform to nonlinear partial differential equations. The method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the Adomian polynomials. We compare the numerical results of the proposed method with those of some available methods. https://jmm.guilan.ac.ir/article_96.html https://jmm.guilan.ac.ir/article_96_27eed1f6a99bbb6f12589fd51a8521f1.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 1 Issue 1 2013 05 01 A modified homotopy perturbation method to periodic solution of a coupled integrable dispersionless equation 68 75 EN Jafar Biazar biazar@guilan.ac.ir Mohammad Hosami mhosami@phd.guilan.ac.ir In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and Pade approximation, known as aftertreatment technique, is proposed. The angular frequencies are compared with the exact frequency. Comparison of the approximated results and exact one shows a good agreement. https://jmm.guilan.ac.ir/article_97.html https://jmm.guilan.ac.ir/article_97_a1b1f301f4ff966292bf0113decf308a.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 1 Issue 1 2013 05 01 On the numerical solution of Urysohn integral equation using Legendre approximation 76 84 EN Ahmad Jafarian jafarian5594@yahoo.com Zahra Esmailzadeh zahra 1324@hotmail.com Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem on the given integral interval, by using the proposed procedure the original integral equation is converted to a linear algebraic system. Now, the solution of the resulting system yields the unknown Legendre coefficients. Finally, two numerical examples are given to show the effectiveness of the proposed method. https://jmm.guilan.ac.ir/article_98.html https://jmm.guilan.ac.ir/article_98_ce285f0f3a6526e5c2e0ee7b4708e1d9.pdf