• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2001.10a
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• pp.138-143
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• 2001

Based on mild slope equation and parabolic approximation the forward diffraction of monochromatic waves by a straight breakwater are studied numerically. The characteristics and effects of stem wave along breakwater and the relations between the stem wave and incident wave angle are discussed.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.19-38
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• 2006

We analyze the spectral collocation approximation for a parabolic partial integrodifferential equations(PIDE) with a weakly singular kernel. The space discretization is based on the spectral collocation method and the time discretization is based on Crank-Nicolson scheme with a graded mesh. We obtain the stability and second order convergence result for fully discrete scheme.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.223-235
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• 2006

By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

• The Journal of the Acoustical Society of Korea
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• v.36 no.1
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• pp.1-11
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• 2017

In this study, novel approximate form of the square-root operator of three dimensional acoustic Parabolic Equation (3D PE) is proposed using a rational approximant for two variables. This form has two advantages in comparison with existing approximation studies of the square-root operator. One is the wide-angle capability. The proposed form has wider angle accuracy to the inclination angle of ${\pm}62^{\circ}$ from the range axis of 3D PE at the bearing angle of $45^{\circ}$, which is approximately three times the angle limit of the existing 3D PE algorithm. Another is that the denominator of our approximate form can be expressed into the product of one-dimensional operators for depth and cross-range. Such a splitting form is very preferable in the numerical analysis in that the 3D PE can be easily transformed into the tridiagonal matrix equation. To confirm the capability of the proposed approximate form, comparative study of other approximation methods is conducted based on the phase error analysis, and the proposed method shows best performance.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.447-456
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• 1997

In this paper an accurate algorithm for the method of successive approximations for near-parabolic orbits is established symbolically. Numerical applications are given for motion predictions at fifteen epochs between the years 66 to 1835 for Halley's comet. and at fifteen epochs between the years 1417 to 1782 for Encke's comet. Comparisons with the standard Gauss method [4] show that the present algorithm is very accurate and efficient for motion pred-ications of near-parabolic orbits.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.28-33
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• 1990

A parabolic model is presented for the effective calculation of refraction-diffraction of regular water while they are propagating on the water of slowly varying sea bed with currents. Parabolic wave equation has been used in the model, which is derived from a mild-slope equation using Pade' approximation. With the corrections of Kirby's (1986) model some numerical experiments were carried out to analyze the model accuracy.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.623-641
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• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.5
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• pp.237-244
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• 2010

In this paper, the dual parabolic cylindrical reflector systems are analyzed as the reflector system for the CATR(Compact Antenna Test Range) facility. The near-field at the test zone of the CATR is calculated by using the PO(Physical Optics) approximation. The CATR has to provide an uniform plane wave with the minimum amplitude and phase ripple and the low cross polarization. Therefore, in this paper, the near-field pattern are calculated, and the ripple and taper of the field and the cross polarization are investigated with the position of the subreflector and the test region. It is confirmed that the analysis results can be used for the design of the CATR with the dual parabolic cylindrical reflector.

• Korean Journal of Optics and Photonics
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• v.11 no.2
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• pp.80-84
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• 2000

Parabolic almninium mlITOr of m.5('||'&'||'cent; 50 nun) was fabncated by a diamond tummg machine. Computer generated hologram (CGH) for the test of parabolic mirror was encoded by binary phase hologram Approximation of curved fringe to line was made by staircase encoding. After fringe data 1ransformed mto a Post Scnpt file. magnified master CGH was printed by a laser printer, and then it reduced to the photographIc film. Parabolic mirror was tested by Twyman-Green interferometer with CGH at VIewing arm. Its experimental result was compared with those of surface profile and auto-collimatIon test, and then the errors were analyzed.