University of GuilanJournal of Mathematical Modeling2345-394X4220160914Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind1171321847ENMeisamJoziFaculty of Sciences, Persian Gulf University, Bushehr, IranSaeedKarimiFaculty of Sciences, Persian Gulf University, Bushehr, IranJournal Article20160914Degenerate 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.<br /><br />University of GuilanJournal of Mathematical Modeling2345-394X4220161025Numerical solution of system of linear integral equations via improvement of block-pulse functions1331591899ENFarshidMirzaeeFaculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, IranJournal Article20161025In this article, a numerical method based onĀ 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.University of GuilanJournal of Mathematical Modeling2345-394X4220161029An efficient nonstandard numerical method with positivity preserving property1611691902ENMohammadMehdizadeh KhalsaraeiDepartment of Mathematics, Faculty of Science, University of Maragheh Maragheh, IranRezaShokri JahandiziDepartment of Mathematics, Faculty of Science, University of Maragheh,
Maragheh, IranJournal Article20161029Classical 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.University of GuilanJournal of Mathematical Modeling2345-394X4220161105Mathematical analysis and pricing of the European continuous installment call option1711851913ENAliBeiranvandFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranAbdolsadehNeisyFaculty of Economics, Allameh Tabataba'i University, Tehran, IranKarimIvazFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranJournal Article20161105In this paper we consider the European continuous installment call option. ThenĀ 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.University of GuilanJournal of Mathematical Modeling2345-394X4220161114Solutions of diffusion equation for point defects1872101942ENOlegVelichkoDepartment of Physics, Belarusian State University of Informatics and Radioelectronics, Minsk, BelarusJournal Article20161114An 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.University of GuilanJournal of Mathematical Modeling2345-394X4220161125Numerical method for a system of second order singularly perturbed turning point problems2112321953ENNeelamegamGeethaDepartment of Mathematics, Bharathidasan University, Tamilnadu, IndiaAyyaduraiTamilselvanDepartment of Mathematics, Bharathidasan University, Tamilnadu, IndiaJoseph StalinChristy RojaDepartment of Mathematics, St. Joseph's college, Tamilnadu, IndiaJournal Article20161125In 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.