J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind On Hammerstein system of Fredholm integral equations Jozi Meisam Faculty of Sciences, Persian Gulf University, Bushehr, Iran Karimi Saeed Faculty of Sciences, Persian Gulf University, Bushehr, Iran 14 09 2016 4 2 117 132 14 09 2016 14 09 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1847.html

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the proposed method is examined.

systems of nonlinear integral equations degenerate kernel Taylor-series expansion nonlinear equations
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Numerical solution of system of linear integral equations via improvement of block-pulse functions Numerical solution of system of linear integral equations Mirzaee Farshid Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran 25 10 2016 4 2 133 159 25 10 2016 25 10 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1899.html

In this article, a numerical method based on  improvement of block-pulse functions (IBPFs) is discussed for solving the system of linear Volterra and Fredholm integral equations. By using IBPFs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. An efficient error estimation and associated theorems for the proposed method are also presented. Some examples are given to clarify the efficiency and accuracy of the method.

system of linear integral equations improvement of block-pulse functions operational matrix vector forms error analysis
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper An efficient nonstandard numerical method with positivity preserving property An efficient nonstandard numerical method Mehdizadeh Khalsaraei Mohammad Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran Shokri Jahandizi Reza Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran 29 10 2016 4 2 161 169 29 10 2016 29 10 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1902.html

Classical explicit finite difference schemes are unsuitable for the solution of the famous Black-Scholes partial differential equation, since they impose severe restrictions on the time step. Furthermore, they may produce spurious oscillations in the solution. We propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. The proposed method is constructed based on a nonstandard discretization of the spatial derivatives and is applicable to Black-Scholes equation in the presence of discontinues initial conditions.

positivity preserving nonstandard finite differences Black-Scholes equation
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Mathematical analysis and pricing of the European continuous installment call option Mathematical analysis and pricing of the European continuous ... Beiranvand Ali Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Neisy Abdolsadeh Faculty of Economics, Allameh Tabataba&#039;i University, Tehran, Iran Ivaz Karim Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran 05 11 2016 4 2 171 185 05 11 2016 05 11 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1913.html

In this paper we consider the European continuous installment call option. Then  its linear complementarity formulation is given. Writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. Finally finite element method is applied to price the European continuous installment call option.

installment option Black-Scholes model free boundary problem variational inequality Finite Element Method
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Solutions of diffusion equation for point defects Solutions of diffusion equation for point defects Velichko Oleg Department of Physics, Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus 14 11 2016 4 2 187 210 14 11 2016 14 11 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1942.html

An analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the Robin-type boundary conditions. The distributions of point defects for different migration lengths of defects have been calculated. The exact analytical solution was used to verify the approximate numerical solution of diffusion equations for vacancies and self-interstitials. Based on the numerical solution obtained, investigation of the diffusion of silicon self-interstitials in a highly doped surface region formed by ion implantation was carried out.

silicon implantation point defect diffusion Modeling
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Numerical method for a system of second order singularly perturbed turning point problems Numerical method for a system of second order singularly perturbed... Geetha Neelamegam Department of Mathematics, Bharathidasan University, Tamilnadu, India Tamilselvan Ayyadurai Department of Mathematics, Bharathidasan University, Tamilnadu, India Christy Roja Joseph Stalin Department of Mathematics, St. Joseph&#039;s college, Tamilnadu, India 25 11 2016 4 2 211 232 25 11 2016 25 11 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1953.html

In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on this mesh. An error estimate is derived by using supremum norm which is \$O(N^{-1}(ln N)^2)\$. Numerical examples are given to validate theoretical results.

singularly perturbed turning point problems boundary value problems finite difference scheme Shishkin mesh and parameter uniform