• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.11-27
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• 2003

A fourth order in time and second order in space scheme using a finite-difference method is developed for the non-linear Boussinesq equation. For the solution of the resulting non-linear system a predictor-corrector pair is proposed. The method is analyzed for local truncation error and stability. The results of a number of numerical experiments for both the single and the double-soliton waves are given.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1725-1739
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• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.7
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• pp.583-586
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• 2013

We consider discrete-time LTI (Linear Time-Invariant) systems with constant input delays. The input delay is modeled by a first-order PdE (Partial difference Equation) and a backstepping transformation is employed to design a predictor feedback controller. The backstepping approach results in the construction of an explicit Lyapunov function, with which we prove the exponential stability of the closed-loop system formed by the predictor feedback. The numerical example demonstrates the design of the predictor feedback controller, and illustrates the validity of the exponential stability.

• Journal of IKEEE
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• v.23 no.4
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• pp.1265-1272
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• 2019

We analyze the robustness of the existing predictor feedback controller for discrete-time linear systems with constant input delays against the structured model uncertainty. By modeling the constant input delay with a first-order PdE (Partial difference Equation), we replace the input delay with the PdE states. By applying a backstepping transformation, we build a target system that enables to construct an explicit Lyapunov function. Constructing the explicit Lyapunov function that covers the entire state variables, we prove the existence of an allowable maximum size of the structured model uncertainty to maintain stability and establish the robustness of the predictor feedback controller. The numerical example demonstrates that the stability of closed-loop system is maintained in the presence of the structured model uncertainty, and verifies the robustness of the predictor feedback controller.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.4
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• pp.296-308
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• 2001

A fully nonlinear Boussinesq equation of Wei et al. is finite differenced by Adams predictor-corrector method. A spatially distributed source function and sponge layers are used to reduce the reflected waves in the domain and wale breaking mechanism is included in the equation. The generated waves are found to be good and the corresponding wale heights are very close to the target values. The shoaling of solitary wave and transformation of regular wave over submerged shelf were simulated successfully. The characteristics of breaking mechanism was identified through the numerical experiment and the results of two dimensional wave propagation test over the spherical shoal showed the importance of nonlinear wave model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.21-25
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• 1998

An algorithm for a solution of ordinary differential equations using a modified corrector in the Adams predictor-corrector method of order four is described. The Lagrange interpolation used in the corrector of the Adams method is replaced partially by the cubic spline interpolation satisfying the first derivative constraints at the two end points. By exhibiting three examples, we show that the proposed method is more effcient when the solution of a differential equation is highly oscillating.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.11
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• pp.2503-2510
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• 2012

This paper proposes a parallel operation intra predictor for H.264/AVC decoder. In previous intra predictor design, common operation units were designed for 17 prediction modes in order to compute more effectively. However, it was designed by analyzing the equation applied to one pixel. So, there are four operation units for computing 16 pixels in a $4{\times}4$ block and they need four cycles. In this paper, the proposed intra predictor contains T3(Three Type Transform) operation unit for parallel operation. It divides 17 modes into 3 types to calculate 16 pixels of a $4{\times}4$ block in only one cycle and needs 16 cycles minimum in 16x16 block. As the result of the experiment, in terms of processing cycle, the performance of proposed intra predictor is 58.95% higher than the previous one.

• Structural Engineering and Mechanics
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• v.48 no.6
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• pp.849-878
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• 2013

This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.8
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• pp.923-931
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• 1999

In this paper, a modeling and a robust time-delay control for the reclaimer are investigated. Supplying the same amount of a raw material throughout the reclamation process from the raw yard to a sinter plant is important to keep the quality of the molten steel uniform in blast furnaces. As the actual parameter values of the reclaimer are not available, the boom rotational dynamics are modeled as a second order differential equation with unknown coefficients. The unknown parameters in the nominal model are estimated using a recursive estimation method. Another important factor in the control design of the reclaimer is the large time-delay in output measurement. Assuming a multiplicative uncertainty, that accounts for both the unstructured uncertainty neglected in the modeling and the structured uncertainty contained in the parameter estimation, a robust Smith predictor is designed. A robust stability criterion for the multiplicative uncertainty is also derived. Following the work of Goodwin et al. [4], a quantifying procedure of the multiplicative uncertainty bound, through experiments , is described. Experimental and simulation results are provided.

• Journal of computational fluids engineering
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• v.9 no.1
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• pp.18-24
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• 2004

The unified simulation for the multiphase flow by predictor-corrector scheme based on CIP method is introduced. In this algorithm, the interface between different phases is identified by a density function and tracked by solving an advection equation. Solid body motion is modeled by the translation and angular motion. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy and capability of proposed algorithm, two dimensional incompressible cavity flow, the motion of a floating ball into water and a single rising bubble by buoyancy force are numerically simulated by the present scheme. As results, it is confirmed that the present scheme gives an efficient, stable and reasonable solution in the multiphase flow problem.