• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.79-86
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• 1998

The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized. In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of applications to the NEACRP PWR rod ejection benchmark problem.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.87-92
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• 1998

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface noes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AEFEN method and the computing time is significantly reduced in comparison with the original AFEN method.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.820-824
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• 2010

Genetic algorithm is known to be an effective method to solve a global nonlinear optimization. However, a huge amount of calculation is needed to improve the dependability of the solution and thus Ga is not adequate for online implementation. In this paper, we propose an online nonlinear system identification scheme which employs population feedback genetic algorithm. The effectiveness of our scheme is shown by several simulations.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.2
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• pp.46.2-46.2
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• 2010

A magnetosonic wave is a longitudinal wave propagating perpendicularly to the magnetic fields and involves compression and rarefaction of the plasma. Lee and Kim (2000) investigated the theoretical solution for the evolution of nonlinear magnetosonic waves in the homogeneous space which adopt the approach of simple waves. We confirm the solution using a one-dimensional MHD code with Total Variation Diminishing (TVD) scheme. Then we apply the solution for the solar wind profiles. We examined the properties of nonlinear waves for the various initial perturbations at near the Lagrangian (L1) point. Also we describe waves steepening process while the shock is being formed by assuming different timescales for a driving source.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• Coupled systems mechanics
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• v.12 no.3
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• pp.221-239
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• 2023

In our research, we have proposed a solid solution for aviation analysis which can ensure the asymptotic stability of coupled nonlinear plants, according to the theoretical solutions and demonstrated method. Because this solution employed the scheme of specific novel theorem of control, the controllers are artificially combined by the parallel distribution computation to have a feasible solution given the random coupled systems with aviation stability analysis. Therefore, we empathize and manually derive the results which shows the utilized lemma and criterion are believed effective and efficient for aircraft structural analysis of composite and nonlinear scenarios. To be fair, the experiment by numerical computation and calculations were explained the perfectness of the methodology we provided in the research.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.297-310
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• 2018

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.385-395
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• 2005

A finite element scheme is considered for the viscous Cahn-Hilliard equation with the nonconstant gradient energy coefficient. The scheme inherits energy decay property and mass conservation as for the classical solution. We obtain the corresponding error estimate using the extended Lax-Richtmyer equivalence theorem.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.835-847
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• 2021

We study behavior of numerical solutions for a nonlinear eigenvalue problem on ℝⁿ that is reduced from a dispersion managed nonlinear Schrödinger equation. The solution operator of the free Schrödinger equation in the eigenvalue problem is implemented via the finite difference scheme, and the primary nonlinear eigenvalue problem is numerically solved via Picard iteration. Through numerical simulations, the results known only theoretically, for example the number of eigenpairs for one dimensional problem, are verified. Furthermore several new characteristics of the eigenpairs, including the existence of eigenpairs inherent in zero average dispersion two dimensional problem, are observed and analyzed.