• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.33-55
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• 2005

The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

• 자연과학논문집
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• 제8권1호
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• pp.5-15
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• 1995

IRR 적응 휠터의 공식오차 방식은 지역 최소값에 관계없이 전역 최소값에 수렴하며 안정성이 높다. 그러나 공식오차 방식은 입력 신호에 잡음이 섞여 경우 예측계수가 바이어스 되는 문제가 있다. 본 논문에서는 사전에 잡음에 대한 지식이 없이 바이어스가 없는 예측계수를 얻을 수 있는 새로운 공식 오차 방식을 위한 알고리즘을 제안한다. 이 알고리즘은 공식오차를 스므딩하는 방식을 이용하여 입력에 추가되는 잡음이 백색잡음인 경우 바이어스 없이 계수를 예측할 수 있다. 시뮬레이션을 통해 새로운 알고리즘이 공식오차의 중요한 장점인 빠른 수렴속도와 안정성을 유지하며 바이어스를 효율적으로 제거함을 볼 수 있다.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.27-43
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• 2002

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

• 대한수학회보
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• 제47권6호
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Journal of Electrical Engineering and Technology
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• 제12권5호
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• pp.1991-2000
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• 2017

This paper presents a compensative microstepping based position control with passive nonlinear adaptive observer for permanent magnet stepper motor. Due to the resistance uncertainties, a position error exists in the steady-state, and a ripple of position error appears during operation. The compensative microstepping is proposed to remedy this problem. The nonlinear controller guarantees the desired currents. The passive nonlinear adaptive observer is designed to estimate the phase resistances and the velocity. The closed-loop stability is proven using input to state stability. Simulation results show that the position error in the steady-state is removed by the proposed method if the persistent excitation conditions are satisfied. Furthermore, the position ripple is reduced, and the Lissajou curve of the phase currents is a circle.

• 제어로봇시스템학회논문지
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• 제15권1호
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• pp.72-81
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• 2009

This paper presents a robust adaptive control method using model reference control strategy against autonomous robot systems with random friction nature. We approximate a nonlinear robot system model by means of a feedback linearization approach to derive nominal control law. We construct a Least Square (LS) based observer to estimate friction dynamics online and then represent a perturbed system model with respect to approximation error between an actual friction and its estimation. Model reference based control design is achieved to implement an auxiliary control in order for reducing control error in practice due to system perturbation. Additionally, we conduct theoretical study to demonstrate stability of the perturbed system model through Lyapunov theory. Numerical simulation is carried out for evaluating the proposed control methodology and demonstrating its superiority by comparing it to a traditional nominal control method.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1205-1219
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• 2011

In this work, a stabilized characteristic finite volume method for the time-dependent Navier-Stokes equations is investigated based on the lowest equal-order finite element pair. The temporal differentiation and advection term are dealt with by characteristic scheme. Stability of the numerical solution is derived under some regularity assumptions. Optimal error estimates of the velocity and pressure are obtained by using the relationship between the finite volume and finite element methods.

• Geomechanics and Engineering
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• 제31권4호
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• pp.339-352
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• 2022

Studying slope stability is an important branch of civil engineering. In this way, engineers have employed machine learning models, due to their high efficiency in complex calculations. This paper examines the robustness of various novel optimization schemes, namely equilibrium optimizer (EO), Harris hawks optimization (HHO), water cycle algorithm (WCA), biogeography-based optimization (BBO), dragonfly algorithm (DA), grey wolf optimization (GWO), and teaching learning-based optimization (TLBO) for enhancing the performance of adaptive neuro-fuzzy inference system (ANFIS) in slope stability prediction. The hybrid models estimate the factor of safety (F_S) of a cohesive soil-footing system. The role of these algorithms lies in finding the optimal parameters of the membership function in the fuzzy system. By examining the convergence proceeding of the proposed hybrids, the best population sizes are selected, and the corresponding results are compared to the typical ANFIS. Accuracy assessments via root mean square error, mean absolute error, mean absolute percentage error, and Pearson correlation coefficient showed that all models can reliably understand and reproduce the F_S behavior. Moreover, applying the WCA, EO, GWO, and TLBO resulted in reducing both learning and prediction error of the ANFIS. Also, an efficiency comparison demonstrated the WCA-ANFIS as the most accurate hybrid, while the GWO-ANFIS was the fastest promising model. Overall, the findings of this research professed the suitability of improved intelligent models for practical slope stability evaluations.

• 대한수학회지
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• 제44권6호
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• pp.1281-1290
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• 2007

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

• 대한수학회지
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• 제51권4호
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• pp.665-678
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• 2014

We present a new space-time discontinuous Galerkin (DG) method for solving the time dependent, positive symmetric hyperbolic systems. The main feature of this DG method is that the discrete equations can be solved semi-explicitly, layer by layer, in time direction. For the partition made of triangle or rectangular meshes, we give the stability analysis of this DG method and derive the optimal error estimates in the DG-norm which is stronger than the $L_2$-norm. As application, the wave equation is considered and some numerical experiments are provided to illustrate the validity of this DG method.