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Rao, R. Nageshwar,Chakravarthy, P. Pramod The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.1
In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.
R. Nageshwar Rao,P. Pramod Chakravarthy 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.1
In this paper, we present an initial value technique for solvingsingularly perturbed differential difference equations with a boundary layerat one end point. Taylor’s series is used to tackle the terms containing shiftprovided the shift is of small order of singular perturbation parameter andobtained a singularly perturbed boundary value problem. This singularlyperturbed boundary value problem is replaced by a pair of initial valueproblems. Classical fourth order Runge–Kutta method is used to solvethese initial value problems. The effect of small shift on the boundarylayer solution in both the cases, i.e., the boundary layer on the left sideas well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability ofthe method.
V. S. MUTHUKUMAR,J. K. KIRAN,JASON REPPERT,R. SATYAJIT,VAMSI KRISHNA,G. NAGESHWAR RAO,S. SIVA RAMA KRISHNAN,S. SIVA SANKARA SAI,K. VENKATARAMANIAH,A. M. RAO 성균관대학교(자연과학캠퍼스) 성균나노과학기술원 2008 NANO Vol.3 No.3
Saturable absorbers and optical limiters have contrary optical transmission properties. We report observations of simultaneous occurrence of both these effects in a nickel sulphide nanoparticle (average dia. ~5 nm) solution and a simultaneous quantitative measurement of both. Intensity dependent nonlinear transmission studies carried out using a 7 ns Nd:YAG laser at 532 nm by the Z-scan method, revealed efficient optical limiting in nickel sulphide nanoparticle suspensions. Induced nonlinear optical scattering was identified to be the mechanism of optical limiting, and absorption at 532 nm was found to saturate. A modification of the conventional Z-scan implementation led to the retrieval of the saturation intensity which is otherwise overshadowed by very strong nonlinear scattering.