eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2016-09-14
4
2
117
132
1847
مقاله پژوهشی
Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind
Meisam Jozi
maisam.j63@gmail.com
1
Saeed Karimi
karimi@pgu.ac.ir
2
Faculty of Sciences, Persian Gulf University, Bushehr, Iran
Faculty of Sciences, Persian Gulf University, Bushehr, Iran
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.
https://jmm.guilan.ac.ir/article_1847_c193bed8fe24050cf187aa6a247bb149.pdf
systems of nonlinear integral equations
degenerate kernel
Taylor-series expansion
nonlinear equations
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2016-10-25
4
2
133
159
1899
مقاله پژوهشی
Numerical solution of system of linear integral equations via improvement of block-pulse functions
Farshid Mirzaee
f.mirzaee@malayeru.ac.ir
1
Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran
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.
https://jmm.guilan.ac.ir/article_1899_e4cbd03a4c25266bf93991e99e8e6b38.pdf
system of linear integral equations
improvement of block-pulse functions
operational matrix
vector forms
error analysis
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2016-10-29
4
2
161
169
1902
مقاله پژوهشی
An efficient nonstandard numerical method with positivity preserving property
Mohammad Mehdizadeh Khalsaraei
muhammad.mehdizadeh@gmail.com
1
Reza Shokri Jahandizi
reza.shokri.j@gmail.com
2
Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran
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.
https://jmm.guilan.ac.ir/article_1902_35066bb8835401ef74cc749daafbb5f2.pdf
positivity preserving
nonstandard finite differences
Black-Scholes equation
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2016-11-05
4
2
171
185
1913
مقاله پژوهشی
Mathematical analysis and pricing of the European continuous installment call option
Ali Beiranvand
a_beiranvand@tabrizu.ac.ir
1
Abdolsadeh Neisy
a_neisy@iust.ac.ir
2
Karim Ivaz
ivaz@tabrizu.ac.ir
3
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Faculty of Economics, Allameh Tabataba'i University, Tehran, Iran
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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.
https://jmm.guilan.ac.ir/article_1913_7c5742fd7191a6a25406a432155c580c.pdf
installment option
Black-Scholes model
free boundary problem
variational inequality
Finite Element Method
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2016-11-14
4
2
187
210
1942
مقاله پژوهشی
Solutions of diffusion equation for point defects
Oleg Velichko
velichkomail@gmail.com
1
Department of Physics, Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
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.
https://jmm.guilan.ac.ir/article_1942_a7ea5d642d6d4b3630417e335fb3ec24.pdf
silicon
implantation
point defect diffusion
Modeling
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2016-11-25
4
2
211
232
1953
مقاله پژوهشی
Numerical method for a system of second order singularly perturbed turning point problems
Neelamegam Geetha
nhgeetha@gmail.com
1
Ayyadurai Tamilselvan
mathats@bdu.ac.in
2
Joseph Stalin Christy Roja
jchristyrojaa@gmail.com
3
Department of Mathematics, Bharathidasan University, Tamilnadu, India
Department of Mathematics, Bharathidasan University, Tamilnadu, India
Department of Mathematics, St. Joseph's college, Tamilnadu, India
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.
https://jmm.guilan.ac.ir/article_1953_a4bc2f09ebf359bf87699982da8549df.pdf
singularly perturbed turning point problems
boundary value problems
finite difference scheme
Shishkin mesh and parameter uniform