• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.601-612
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• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.425-440
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• 2010

Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.

• Journal of the Korea Society for Simulation
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• v.2 no.1
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• pp.55-66
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• 1993

Although the Pontryagin's maximum principle theory is widely applied in control problems, its contribution to the solution procedure have been restricted just to figure out the rough picture of true solutions, probably due to the complexity of the two-point boundary value problems. This paper discusses a numerical approach to solve the control problems in connection with the two -point boundary value problems. A model of labor management negotiation during a strike has been constructed and solved explicitly by us of DVCPR subroutine introduced in IMSL. The results have been turned out that the management is better increase wage very slowly during the strike period, while , on the labor side, it is more effective to show the high intensity of demonstration against the company at the outset and gradually decrease it.

• Proceedings of the Korea Society for Simulation Conference
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• 1993.10a
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• pp.3-3
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• 1993

Although tile Pontryagin's maxlmum principle theory is widely applied in control problems, its contribution to the solution procedure have been restricted just to figure out the rough picture of true solutions, probably due to the complexity of the two-point boundary value problems.This paper discusses the numerical approach to solve the control problems in connection with the two-point boundary value problems. A model of labor-management negotiatulon during a strike has been constructed and solved explicitly by use of DVCPR subroutine introduced in IMSL. The results have been turned out that the management is better increase wage very slowly during the strike period, while, on the labor side, it is more effective to show the high intensity of demonstration against the company at the outset and gradually decrease it.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• Journal of electromagnetic engineering and science
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• v.14 no.3
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• pp.273-277
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• 2014

In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

• Journal of the Korean Geographical Society
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• v.49 no.3
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• pp.423-437
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• 2014

Districting is a spatial decision making process to make a new regional framework for affecting human activities. Natural barriers such as rivers and mountains located within a reorganized district may reduce the efficiency of reorganized human activities. This implies that it is necessary to consider boundary characteristics in a districting process. The purpose of this research is to develop a new spatial optimization model based on boundary characteristics for districting problems. The boundary characteristics are evaluated as continuous value expressing the possibility of combining adjacent two basic spatial units rather than a dichotomous value with 1 or 0 and are defined as an objective function in the model. In addition, the model has explicitly formulated contiguity constraints as well as constraints enforcing demand balance among districts such as population and area. The boundary attributes are categorized into physical and relational characteristics. Suitability analysis is used to combine various variables related to each boundary characteristic and to evaluate the coupling possibility between two neighboring basic units. The model is applied to an administrative redistricting problem. The analytical results demonstrate that various boundary characteristics could be modeled in terms of mixed integer programming (MIP).

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.715-725
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• 2013

In this paper, a finite difference scheme for a two-point boundary value problem of 2nth-order ordinary differential equations is presented. The convergence and uniqueness of the solution for the scheme are proved by means of theories on matrix eigenvalues and norm. Numerical examples show that our method is very simple and effective, and that this method can be used effectively for other types of boundary value problems.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.477-488
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• 2012

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the mixed interface condition, controlled by a parameter, can optimize SAM's convergence rate. In [8], one introduced the two-layer multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. In this paper, we present a method which utilizes the one-dimensional result to get the optimal convergence rate for the two-dimensional problem.