فهرست مطالب

Mathematical Modeling - Volume:4 Issue:2, 2017
  • Volume:4 Issue:2, 2017
  • تاریخ انتشار: 1395/11/12
  • تعداد عناوین: 6
|
  • Meisam Jozi, Saeed Karimi * Pages 117-132
    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.
    Keywords: systems of nonlinear integral equations, degenerate kernel, Taylor, series expansion, nonlinear equations
  • Farshid Mirzaee* Pages 133-159
    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.
    Keywords: system of linear integral equations, improvement of block-pulse functions, operational matrix, vector forms, error analysis
  • Mohammad Mehdizadeh Khalsaraei *, Reza Shokri Jahandizi Pages 161-169
    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.
    Keywords: positivity preserving, nonstandard finite differences, Black-Scholes equation
  • Ali Beiranvand, Abdolsadeh Neisy *, Karim Ivaz Pages 171-185
    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.
    Keywords: installment option, Black-Scholes model, free boundary problem, variational inequality, finite element method
  • Oleg Velichko* Pages 187-210
    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.
    Keywords: silicon, implantation, point defect diffusion, modeling
  • Neelamegam Geetha, Ayyadurai Tamilselvan*, Joseph Stalin Christy Roja Pages 211-232
    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 (lnN) 2 ) O(N−1(ln⁡N)2). Numerical examples are given to validate theoretical results.
    Keywords: singularly perturbed turning point problems, boundary value problems, finite difference scheme, Shishkin mesh, parameter uniform