A new model of (I+S)-type preconditioner for system of linear equations
Hashem
Saberi Najafi
author
Seyyed Ahmad
Edalatpanah
author
Amir Hossein
Refahi Sheikhani
author
text
article
2013
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
1
v.
Issue 1
no.
2013
1
14
https://jmm.guilan.ac.ir/article_93_b4db128b77ca7337ef098743583ad747.pdf
Global conjugate gradient method for solving large general Sylvester matrix equation
Saeed
Karimi
author
text
article
2013
eng
In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A \in R^{n\times n}$ , $C \in R^{n\times n}$ , $B \in R^{s\times s}$ and $D \in R^{s\times s}$ are given matrices and $X \in R^{s\times s}$ 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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
1
v.
Issue 1
no.
2013
15
27
https://jmm.guilan.ac.ir/article_94_1e1d28447d734ae7d2d734743b7e1042.pdf
Solving a class of nonlinear two-dimensional Volterra integral equations by using two-dimensional triangular orthogonal functions
Farshid
Mirzaee
author
text
article
2013
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
1
v.
Issue 1
no.
2013
28
40
https://jmm.guilan.ac.ir/article_95_1fd90cc636e55d438249335afa4f5fa4.pdf
Application of Laplace decomposition method for Burgers-Huxley and Burgers-Fisher equations
Mohammad Reza
Yaghouti
author
Ali
Zabihi
author
text
article
2013
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
1
v.
Issue 1
no.
2013
41
67
https://jmm.guilan.ac.ir/article_96_27eed1f6a99bbb6f12589fd51a8521f1.pdf
A modified homotopy perturbation method to periodic solution of a coupled integrable dispersionless equation
Jafar
Biazar
author
Mohammad
Hosami
author
text
article
2013
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
1
v.
Issue 1
no.
2013
68
75
https://jmm.guilan.ac.ir/article_97_a1b1f301f4ff966292bf0113decf308a.pdf
On the numerical solution of Urysohn integral equation using Legendre approximation
Ahmad
Jafarian
author
Zahra
Esmailzadeh
author
text
article
2013
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
1
v.
Issue 1
no.
2013
76
84
https://jmm.guilan.ac.ir/article_98_ce285f0f3a6526e5c2e0ee7b4708e1d9.pdf