• Communications for Statistical Applications and Methods
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• v.23 no.1
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• pp.21-32
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• 2016

We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Advances in aircraft and spacecraft science
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• v.1 no.1
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• pp.93-123
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• 2014

A variational asymptotic composite beam model has been developed for thermoelastic analysis. Composite beams, including sandwich structure and laminates, under different boundary conditions are examined. Previously developed beam model, which is based on variational-asymptotic method, is extended to incorporate temperature-dependent materials experiencing large temperature changes. The recovery relations have been derived so that the temperatures, heat fluxes, stresses, and strains can be recovered over the cross-section. The present theory is implemented into the computer program VABS (Variational Asymptotic Beam Sectional analysis). Numerical results are compared with the 3D analysis for the purpose of demonstrating advantages of the present theory and use of VABS.

• Structural Engineering and Mechanics
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• v.12 no.2
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• pp.215-230
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• 2001

In this paper, an asymptotic two-scale method is developed for solving vibration problem of long periodic structures. Such eigenmodes appear as a slow modulations of a periodic one. For those, the present method splits the vibration problem into two small problems at each order. The first one is a periodic problem and is posed on a few basic cells. The second is an amplitude equation to be satisfied by the envelope of the eigenmode. In this way, one can avoid the discretisation of the whole structure. Applying the Floquet method, the boundary conditions of the global problem are determined for any order of the asymptotic expansions.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.937-948
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• 2011

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.483-492
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• 2008

The k-fold pseudo-Newton's method is proposed and its convergence behavior is investigated near a simple zero. The order of convergence is proven to be at least k + 2. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. High-precison numerical results are successfully implemented via Mathematica and illustrated for various examples.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.635-643
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• 2002

The asymptotic behaviour of the solutions of initial - boundary value problem for a class of nonlinear parabolic differential - functional equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.597-603
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• 2010

We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.185-196
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• 1999

This paper is concerned with investigating the global asymptotic behavior of the solution to a nonlinear wave equation with variable coefficients. noreover an estimate of the rate of decay of the solution is obtained.