• Title, Summary, Keyword: asymptotic method

### Allowable limit of physical optics in radar cross section analysis of edge shape (가장자리 형상의 레이더 반사 면적 해석에서 물리광학기법의 적용 한계)

• Baek, Sang-Min
• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.46 no.1
• /
• pp.78-85
• /
• 2018
• As a numerical analysis technique to predict the radar cross section of an aircraft, a full wave method or an asymptotic method is mainly used. The full-wave method is expected to be relatively accurate compared with the asymptotic method. The asymptotic method is numerically efficient, and it is more widely used in the RCS analysis. However, the error that occurs when estimating the RCS using the asymptotic method is difficult to predict easily. In this paper, we analyze the allowable limits of physical optics by constructing a wedge-cylinder model and comparing the RCS prediction results between the method of moment and physical optics while changing the edge shape. Finally, this study proposes a criterion for allowable limit of physical optics in the RCS estimation.

### Asymptotic computation of Greeks under a stochastic volatility model

• Park, Sang-Hyeon;Lee, Kiseop
• Communications for Statistical Applications and Methods
• /
• v.23 no.1
• /
• pp.21-32
• /
• 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.

### A variational asymptotic approach for thermoelastic analysis of composite beams

• Wang, Qi;Yu, Wenbin
• Advances in aircraft and spacecraft science
• /
• v.1 no.1
• /
• pp.93-123
• /
• 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.

### AN ASYMPTOTIC FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS OF CONVECTION-DIFFUSION TYPE WITH DISCONTINUOUS SOURCE TERM

• Babu, A. Ramesh;Ramanujam, N.
• Journal of applied mathematics & informatics
• /
• v.26 no.5_6
• /
• pp.1057-1069
• /
• 2008
• We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

### THE METHOD OF ASYMPTOTIC INNER BOUNDARY CONDITION FOR SINGULAR PERTURBATION PROBLEMS

• Andargie, Awoke;Reddy, Y.N.
• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.937-948
• /
• 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.

### Vibrations of long repetitive structures by a double scale asymptotic method

• Daya, E.M.;Potier-Ferry, M.
• Structural Engineering and Mechanics
• /
• v.12 no.2
• /
• pp.215-230
• /
• 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.

### ASYMPTOTIC ERROR ANALYSIS OF k-FOLD PSEUDO-NEWTON'S METHOD LOCATING A SIMPLE ZERO

• Kim, Young Ik
• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.4
• /
• pp.483-492
• /
• 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.

### ASYMPTOTIC SOLUTIONS OF FOURTH ORDER CRITICALLY DAMPED NONLINEAR SYSTEM UNDER SOME SPECIAL CONDITIONS

• Lee, Keonhee;Shanta, Shewli Shamim
• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.413-426
• /
• 2008
• An asymptotic solution of a fourth order critically damped nonlinear differential system has been found by means of extended Krylov-Bogoliubov-Mitropolskii (KBM) method. The solutions obtained by this method agree with those obtained by numerical method. The method is illustrated by an example.

### On asymptotic stability in nonlinear differential system

• An, Jeong-Hyang
• Journal of the Korean Data and Information Science Society
• /
• v.21 no.3
• /
• pp.597-603
• /
• 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.

### Asymptotic Distribution of the Estimator for Rotation in Orientation-Shift Model on the Sphere

• Shin, Yang-Kyu
• Journal of the Korean Data and Information Science Society
• /
• v.10 no.1
• /
• pp.19-27
• /
• 1999
• An orientation-shift model for unit random vectors in $R^3$ is defined. The Euler angles are introduced to parametrize orientation-shifts and their moment estimators are found. Through the analytic perturbation method, the asymptotic distributions of the estimators are obtained.