• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.5 no.1
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• pp.40-45
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• 2002

The calculation of earthwork plays a major role in the planning and design phases of many civil engineering projects, such as seashore reclamation; thus, improving the accuracy of earthwork calculation has become very important. In this paper, we propose an algorithm for finding a cubic spline surface with the free boundary conditions, which interpolates the given three-dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors, especially those concerned with accuracy of volume computations. The mathematical models of the conventional methods have a common drawback: the modeling curves form peak points at the joints. To avoid this drawback, the cubic spline polynomial is chosen as the mathematical model of the new method. In this paper, we propose an algorithm of finding a spline surface, which interpolates the given data, and an appropriate method to calculate the earthwork. We present some computational results that show the proposed method, of the Maple program, provides better accuracy than the method presented by Chen and Lin.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.355-360
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• 2000

This paper presents properties of piecewise cubic B-spline function and Rayleigh-Ritz method to compute the smallest eigenvales. In order to compute the smallest eigenvalues, Rayleigh quotient approach is used and four different types of finite element approximating functions corresponding to the statical deflection curve, spanned by the linearly independent set of piecewise cubic B-spline functions with equally spaced 5 knots from a partion of [0, 1], each satisfying homogeneous boundary conditions with constraining effects are used to compute the smallest eigenvalues for a Sturm-Lionville boundary equations of u"＋ λ²u＝0, u(0.0)＝u(0.0)＝0, 0≤x≤1.0.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.759-770
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• 1998

In this paper we use uniform cubic spline polynomials to derive some new consistency relations. These relations are then used to develop a numerical method for computing smooth approxi-mations to the solution and its first second as well as third derivatives for a second order boundary value problem. The proesent method out-performs other collocations finite-difference and splines methods of the same order. numerical illustratiosn are provided to demonstrate the practical use of our method.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.3
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• pp.33-38
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• 2011

A cubic spline trajectory planner with arc-length parameter is formulated with estimation by summing up to the 3rd order in Taylor's expansion. The PVAJT motion planning is presented to reduce trajectory calculation time at every cycle time of servo control loop so that it is able to generate cubic spline trajectory in real time. This method can be used to more complex spline trajectory. Several case studies are executed with different values of cycle time and sampling time, and showed the advantages of the PVAJT motion planner. A DSP-based motion controller is designed to implement the PVAJT motion planning.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.371-386
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• 2001

In this work we investigate the finite element preconditioning method for the $C^1$-cubic spline collocation discretizations for an elliptic operator A defined by $Au := -{\Delta}u + a_1u_x+a_2u_y+a_0u$ in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.

• Industrial Engineering and Management Systems
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• v.9 no.4
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• pp.323-338
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• 2010

In this paper, we introduce the implied volatility from Black-Scholes model and suggest a model for constructing implied volatility surfaces by using the two-dimensional cubic (bi-cubic) spline. In order to utilize a spline method, we acquire grid (knot) points. To this end, we first extract implied volatility curves weighted by trading contracts from market option data and calculate grid points from the extracted curves. At this time, we consider several conditions to avoid arbitrage opportunity. Then, we establish an implied volatility surface, making use of the two-dimensional cubic spline method with previously estimated grid points. The method is shown to satisfy several properties of the implied volatility surface (smile, skew, and flattening) as well as avoid the arbitrage opportunity caused by simple match with market data. To show the merits of our proposed method, we conduct simulations on market data of S&P500 index European options with reasonable and acceptable results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.5
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• pp.1168-1175
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• 1995

The application of cubic spline is presented for basic curve (DRD motion) of cam motion. The purpose of this paper is to achieve better dynamic characteristics than general cam curves. A cubic spline is a piecewise function that is continuous in displacement, velocity and acceleration. The best cam curve is obtained by changing the weights of the object function. So the method can be used to any machine system case by case. For the proposed object function, the result has improved all characteristics such as velocity, acceleration and jerk compared with that of the modified sine curve.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.11-17
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• 1990

Dirichlet boundary value problems originated from unsteady deep water wave propagation are transformed to Boundary Intergral Equation Methods by use of a free surface Green's function and the integral equations are discretized by a cubic spline element method. In order to enhance the stability of the numerical model based on the derived Fredholm integral equation of 1 st kind, the method by Hsiao and MacCamy (1973) is employed. The numerical model is tested against exact solutions for two cases and the model shows very good accuracy.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.1
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• pp.3-10
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• 1990

Hull form can be described numerically by two approaches, one is to describe a hull form with a set of curves("curve approach"), and the other is to describe it with surfaces directly("surface approach"). This paper describes the numerical definition scheme of hull form using curve approach method which defines the hull form by a set of curves consisting of 2-dimensional transverse section curves and 3-dimensional longitudinal curves. A set of curves in the hull form definition scheme is described by the modified cubic spline which modified the general parametric cubic spline in order to ensure a very smooth curvature distribution within the curve segment even though a curve segment has large tangent angle at its end points. Illustrative examples are given showing the application of the method to represent the hull form of SWATH ship and oceanographic research vessel. Also, examples for hull form transformation are shown by using this method connected with transformation technique.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.153-164
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• 1996

An $O(h^4)$ cubic spline collocation method for biharmonic equation with a special boundary conditions is formulated and a fast direct method is proposed for the linear system arising when the cubic spline collocation method is employed. This method requires $O(N^2\;{\log}\;N)$ arithmatic operations over an $N{\times}N$ uniform partition.