Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind
Meisam
Jozi
Faculty of Sciences, Persian Gulf University, Bushehr, Iran
author
Saeed
Karimi
Faculty of Sciences, Persian Gulf University, Bushehr, Iran
author
text
article
2016
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
4
v.
2
no.
2016
117
132
https://jmm.guilan.ac.ir/article_1847_c193bed8fe24050cf187aa6a247bb149.pdf
Numerical solution of system of linear integral equations via improvement of block-pulse functions
Farshid
Mirzaee
Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran
author
text
article
2016
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
4
v.
2
no.
2016
133
159
https://jmm.guilan.ac.ir/article_1899_e4cbd03a4c25266bf93991e99e8e6b38.pdf
An efficient nonstandard numerical method with positivity preserving property
Mohammad
Mehdizadeh Khalsaraei
Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran
author
Reza
Shokri Jahandizi
Department of Mathematics, Faculty of Science, University of Maragheh,
Maragheh, Iran
author
text
article
2016
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
4
v.
2
no.
2016
161
169
https://jmm.guilan.ac.ir/article_1902_35066bb8835401ef74cc749daafbb5f2.pdf
Mathematical analysis and pricing of the European continuous installment call option
Ali
Beiranvand
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
author
Abdolsadeh
Neisy
Faculty of Economics, Allameh Tabataba'i University, Tehran, Iran
author
Karim
Ivaz
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
author
text
article
2016
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
4
v.
2
no.
2016
171
185
https://jmm.guilan.ac.ir/article_1913_7c5742fd7191a6a25406a432155c580c.pdf
Solutions of diffusion equation for point defects
Oleg
Velichko
Department of Physics, Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
author
text
article
2016
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
4
v.
2
no.
2016
187
210
https://jmm.guilan.ac.ir/article_1942_a7ea5d642d6d4b3630417e335fb3ec24.pdf
Numerical method for a system of second order singularly perturbed turning point problems
Neelamegam
Geetha
Department of Mathematics, Bharathidasan University, Tamilnadu, India
author
Ayyadurai
Tamilselvan
Department of Mathematics, Bharathidasan University, Tamilnadu, India
author
Joseph Stalin
Christy Roja
Department of Mathematics, St. Joseph's college, Tamilnadu, India
author
text
article
2016
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
4
v.
2
no.
2016
211
232
https://jmm.guilan.ac.ir/article_1953_a4bc2f09ebf359bf87699982da8549df.pdf