• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권3호
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• pp.194-206
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• 2023

We present families of nonlinear transformations useful for numerical evaluation of weakly singular integrals. First, for end-point singular integrals, we define a prototype function with some appropriate features and then suggest a family of transformations. In addition, for interior-point singular integrals, we develop a family of nonlinear transformations based on the aforementioned prototype function. We take some examples to explore the efficiency of the proposed nonlinear transformations in using the Gauss-Legendre quadrature rule. From the numerical results, we can find the superiority of the proposed transformations compared to some existing transformations, especially for the integrals with high singularity strength.

• 한국해안·해양공학회논문집
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• 제20권1호
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• pp.121-127
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• 2008

비선형의 정도에 따른 Boussinesq 모형의 특성을 비교하기 위해 약비선형 모형인 MIKE21 BW 모듈과 완전비선형 모형인 FUNWAVE 모형을 이용하여 수치실험을 수행하였다. 진폭별 조파실험, 심해 파형경사별 천수실험 그리고 사주 지형상의 파랑 전파실험을 수행하였고, 이상의 실험을 통해 비선형성이 부각되는 천해역에서 비선형 모형의 중요성을 확인하였다. 특히 완전 비선형 모형이 약비선형 모형에 비해 비대칭 파형의 재현성이 우수하고, 천수현상에 따른 파고의 증가가 상대적으로 크게 나타나는 모형 간 특성을 확인하였다.

• 대한수학회논문집
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• 제27권1호
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• pp.97-106
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• 2012

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.565-580
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• 2021

In this paper, first of all we prove a fixed point theorem for 𝜓_∫𝜑-weakly contractive mapping. Next, we prove some common fixed point theorems for a pair of weakly compatible self maps along with E.A. property and (CLR) property. An example is also given to support our results.

• 대한수학회지
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• 제41권6호
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• pp.957-976
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• 2004

It is well known that the application of the nonlinear coordinate transformations is useful for efficient numerical evaluation of weakly singular integrals. In this paper, we consider the trapezoidal rule combined with a nonlinear transformation $\Omega$$_{m}$(b;$\chi$), containing a parameter b, proposed first by Yun [14]. It is shown that the trapezoidal rule with the transformation $\Omega$$_{m}$(b;$\chi$), like the case of the Gauss-Legendre quadrature rule, can improve the asymptotic truncation error by using a moderately large b. By several examples, we compare the numerical results of the present method with those of some existing methods. This shows the superiority of the transformation $\Omega$$_{m}$(b;$\chi$).TEX>).

• Journal of Advanced Research in Ocean Engineering
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• 제3권2호
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• pp.83-101
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• 2017

In this study, the added resistances of the large container ship in head and oblique seas are evaluated using a time-domain Rankine panel method. The mean forces and moments are computed by the near-field method, namely, the integration of the second-order pressure directly on the ship surface. Furthermore, a weakly nonlinear approach in which the nonlinear restoring and Froude-Krylov forces on the exact wetted surface of a ship are included in order to examine the effects of amplitudes of waves on ship motions and added resistances. The computation results for various advance speeds and heading angles are validated by comparing with the experimental data, and the validation shows reasonable consistency. Nevertheless, there exist discrepancies between the numerical and experimental results, especially for a shorter wave length, a higher advance speed, and stern quartering seas. Therefore, the accuracies of the linear and weakly nonlinear methods in the evaluation of the mean drift forces and moments are also discussed considering the characteristics of the hull such as the small incline angle of the non-wall-sided stern and the fine geometry around the high-nose bulbous bow.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.271-287
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• 2022

In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d^*) satisfying the following ξ-weakly expansive condition: d^*(𝒫c, 𝒫d) ≥ d^* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.877-888
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• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회(2)
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• pp.1319-1320
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• 2005

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.257-265
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• 2011

In this paper, we first prove a common fixed point theorem for generalized nonlinear contraction mappings in complete metric spaces there by generalizing and extending some known results. Then we present this result in the context of ordered metric spaces by using monotone non-decreasing mapping.