2018-12-11T15:54:03Z
https://jmm.guilan.ac.ir/?_action=export&rf=summon&issue=391
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2016
4
2
Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind
Meisam
Jozi
Saeed
Karimi
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
2016
09
14
117
132
https://jmm.guilan.ac.ir/article_1847_c193bed8fe24050cf187aa6a247bb149.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2016
4
2
Numerical solution of system of linear integral equations via improvement of block-pulse functions
Farshid
Mirzaee
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
2016
10
25
133
159
https://jmm.guilan.ac.ir/article_1899_e4cbd03a4c25266bf93991e99e8e6b38.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2016
4
2
An efficient nonstandard numerical method with positivity preserving property
Mohammad
Mehdizadeh Khalsaraei
Reza
Shokri Jahandizi
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
2016
10
29
161
169
https://jmm.guilan.ac.ir/article_1902_35066bb8835401ef74cc749daafbb5f2.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2016
4
2
Mathematical analysis and pricing of the European continuous installment call option
Ali
Beiranvand
Abdolsadeh
Neisy
Karim
Ivaz
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
2016
11
05
171
185
https://jmm.guilan.ac.ir/article_1913_7c5742fd7191a6a25406a432155c580c.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2016
4
2
Solutions of diffusion equation for point defects
Oleg
Velichko
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
2016
11
14
187
210
https://jmm.guilan.ac.ir/article_1942_a7ea5d642d6d4b3630417e335fb3ec24.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2016
4
2
Numerical method for a system of second order singularly perturbed turning point problems
Neelamegam
Geetha
Ayyadurai
Tamilselvan
Joseph Stalin
Christy Roja
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
2016
11
25
211
232
https://jmm.guilan.ac.ir/article_1953_a4bc2f09ebf359bf87699982da8549df.pdf