• East Asian mathematical journal
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• 제36권4호
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• pp.437-454
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• 2020

The purpose of this study is to develop a mathematical assessment and correction materials according to the mathematics learning hierarchy. The scope of the study is set to 'function' in 7th grade of middle school. The researchers developed a draft of the mathematical assessment and correction materials based on the mathematics learning hierarchy through the pilot test and the expert review. Using the results of the expert review, the researchers modified and supplemented the math assessment and correction materials to produce the final version. The mathematics assessment and correction material developed in this study is expected to build an effective guidance system for students with mathematics deficits. In addition, by presenting a mathematical assessment and correction materials to the teachers in the field, it is possible to reduce the effort for the management of underachievers and to provide guidance for the education of students with a lack of math learning.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.301-311
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• 2015

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al. [8, 9]. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems [1].

• 대한수학회지
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• 제49권3호
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• pp.549-569
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• 2012

In this paper asymptotic error expansions for mixed finite element approximations to a class of second order elliptic optimal control problems are derived under rectangular meshes, and the Richardson extrapolation of two different schemes and interpolation defect correction can be applied to increase the accuracy of the approximations. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators of the mixed finite element method for optimal control problems.

• 대한수학회논문집
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• 제24권3호
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• pp.395-395
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• 2009

• East Asian mathematical journal
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• 제17권2호
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• pp.297-301
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• 2001

• 대한수학회지
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• 제50권5호
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• East Asian mathematical journal
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• 제34권3호
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• pp.239-248
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• 2018

In this paper, we derive a closed-form formula of a second-order approximation for a European corrected option price under stochastic elasticity of variance model mentioned in Kim et al. (2014) [1] [J.-H. Kim, J Lee, S.-P. Zhu, S.-H. Yu, A multiscale correction to the Black-Scholes formula, Appl. Stoch. Model. Bus. 30 (2014)]. To find the explicit-form correction to the option price, we use Mellin transform approaches.

• 충청수학회지
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• 제16권2호
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• pp.75-78
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• 2003

The Tychonoff product theorem is one of the most fundamental theorems in general topology. As is well-known, the proof of the Tychonoff product theorem relies on the axiom of choice. The converse was also conjectured by S. Kakutani and Kelley [1] then resolved this conjecture in his historical short note on 1950. However, the original proof due to Kelley has a flaw. According to this observation, we provide a correction of the proof in this paper.

• East Asian mathematical journal
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• 제40권1호
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• pp.109-118
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• 2024

This paper proposes a numerical method based on domain decomposition to find approximate solutions for one-dimensional convection-diffusion equations with Neumann boundary conditions. First, the equations are transformed into convection-diffusion equations with Dirichlet conditions. Second, the author introduces the Prediction/Correction Domain Decomposition (PCDD) method and estimates errors for the interface prediction scheme, interior scheme, and correction scheme using known error estimations. Finally, the author compares the PCDD algorithm with the fully explicit scheme (FES) and the fully implicit scheme (FIS) using three examples. In comparison to FES and FIS, the proposed PCDD algorithm demonstrates good results.

• Kyungpook Mathematical Journal
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• 제52권2호
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• pp.167-177
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• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.