University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
4
2
2016
09
14
Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind
117
132
EN
Meisam
Jozi
Faculty of Sciences, Persian Gulf University, Bushehr, Iran
maisam.j63@gmail.com
Saeed
Karimi
Faculty of Sciences, Persian Gulf University, Bushehr, Iran
karimi@pgu.ac.ir
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
https://jmm.guilan.ac.ir/article_1847.html
https://jmm.guilan.ac.ir/article_1847_c193bed8fe24050cf187aa6a247bb149.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
4
2
2016
10
25
Numerical solution of system of linear integral equations via improvement of block-pulse functions
133
159
EN
Farshid
Mirzaee
Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran
f.mirzaee@malayeru.ac.ir
In 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.
system of linear integral equations,improvement of block-pulse functions,operational matrix,vector forms,error analysis
https://jmm.guilan.ac.ir/article_1899.html
https://jmm.guilan.ac.ir/article_1899_e4cbd03a4c25266bf93991e99e8e6b38.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
4
2
2016
10
29
An efficient nonstandard numerical method with positivity preserving property
161
169
EN
Mohammad
Mehdizadeh Khalsaraei
Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran
muhammad.mehdizadeh@gmail.com
Reza
Shokri Jahandizi
Department of Mathematics, Faculty of Science, University of Maragheh,
Maragheh, Iran
reza.shokri.j@gmail.com
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
https://jmm.guilan.ac.ir/article_1902.html
https://jmm.guilan.ac.ir/article_1902_35066bb8835401ef74cc749daafbb5f2.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
4
2
2016
11
05
Mathematical analysis and pricing of the European continuous installment call option
171
185
EN
Ali
Beiranvand
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
a_beiranvand@tabrizu.ac.ir
Abdolsadeh
Neisy
Faculty of Economics, Allameh Tabataba'i University, Tehran, Iran
a_neisy@iust.ac.ir
Karim
Ivaz
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
ivaz@tabrizu.ac.ir
In 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.
installment option,Black-Scholes model,free boundary problem,variational inequality,finite element method
https://jmm.guilan.ac.ir/article_1913.html
https://jmm.guilan.ac.ir/article_1913_7c5742fd7191a6a25406a432155c580c.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
4
2
2016
11
14
Solutions of diffusion equation for point defects
187
210
EN
Oleg
Velichko
Department of Physics, Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
velichkomail@gmail.com
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
https://jmm.guilan.ac.ir/article_1942.html
https://jmm.guilan.ac.ir/article_1942_a7ea5d642d6d4b3630417e335fb3ec24.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
4
2
2016
11
25
Numerical method for a system of second order singularly perturbed turning point problems
211
232
EN
Neelamegam
Geetha
Department of Mathematics, Bharathidasan University, Tamilnadu, India
nhgeetha@gmail.com
Ayyadurai
Tamilselvan
Department of Mathematics, Bharathidasan University, Tamilnadu, India
mathats@bdu.ac.in
Joseph Stalin
Christy Roja
Department of Mathematics, St. Joseph's college, Tamilnadu, India
jchristyrojaa@gmail.com
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
https://jmm.guilan.ac.ir/article_1953.html
https://jmm.guilan.ac.ir/article_1953_a4bc2f09ebf359bf87699982da8549df.pdf