• Journal of applied mathematics & informatics
• /
• 제38권1_2호
• /
• pp.113-132
• /
• 2020

In this paper, a class of linear second order singularly perturbed delay differential turning point problems containing a small delay (or negative shift) on the reaction term and when the solution of the problem exhibits twin boundary layers are examined. A hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the problem. We proved that the method is almost second order ε-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results.

• 한국초전도ㆍ저온공학회논문지
• /
• 제5권2호
• /
• pp.66-70
• /
• 2003

Transient magnetic diffusion process in a melt-cast Bi2Sr2CaCu20X(Bi-2212) tube was studied by experimental and numerical analyses. The transient diffusion partial differential equation is transformed into an ordinary differential equation by integral method. The penetration depth of magnetic field into a superconducting tube is obtained by solving the differential equation numerically. The results show that the penetration depth as a function of time which is somewhat different from the results by Bean's critical state model. The reason of the difference between the present results and that of Bean's model is discussed and compared in this paper. This experiment measure the magnetic flux density in the supercondutor after supply direct-current of Bi-2212 rounded by copper coil. This study was discussed of valid of a previous numerical solution which is compared by the penetrate time and the magnetic flux density difference of between the present results and the numerical solution.

• 한국콘크리트학회:학술대회논문집
• /
• 한국콘크리트학회 1998년도 봄 학술발표회 논문집(I)
• /
• pp.397-402
• /
• 1998

The objectives of this paper are to estimate differential column Shortening and to determine appropreate compensation amount in 52 story Amatapura Apartment in Indonesia. for this, a computer program based on PCA and CEB-FIP code is developed. The results show that Elastic and Creep strain are the main factors of column shortening and the maximum differential shortening is appeared near the middle of the building height. The results between field survey and estimation have some difference, the most influential factor of the difference can be lateral restraints provided by horizontal members, which cannot be handled in this developed program. Hence introducing the modification factors from various field survey, this program can be used properly in design and construction procedures.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제17권4호
• /
• pp.221-237
• /
• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Journal of applied mathematics & informatics
• /
• 제39권5_6호
• /
• pp.623-641
• /
• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• Journal of applied mathematics & informatics
• /
• 제41권2호
• /
• pp.439-448
• /
• 2023

We introduce several higher-order (p, q)-differential equation of which are related to (p, q)-Bernoulli polynomials. We also find some relations between (p, q)-Bernoulli, (p, q)-Euler, and (p, q)-Genocchi polynomials.

• 한국콘크리트학회:학술대회논문집
• /
• 한국콘크리트학회 1993년도 봄 학술발표회 논문집
• /
• pp.142-147
• /
• 1993

In the reinforced concrete structure, as the height of building structure increases, the accurate estimation of differential column shortening is important factor in the structural design. In this study, the analysis of column shortening is applied to 36-story building structure to be built in time. As a result, it may found that, as the difference of compressive stress become larger, differential shortening effect due to creep and shrinkage are more signicant factor to structural designer.

• Journal of applied mathematics & informatics
• /
• 제34권5_6호
• /
• pp.421-434
• /
• 2016

The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.

• 대한수학회지
• /
• 제61권5호
• /
• pp.975-995
• /
• 2024

In this paper, we utilize Nevanlinna theory to study the existence and forms of solutions for quadratic trinomial complex partial differential-difference equations of the form aF² + 2ωFG + bG² = exp(g), where ab ≠ 0, ω ∈ ℂ with ω² ≠ 0, ab and g is a polynomial in ℂⁿ. In order to achieve a comprehensive and thorough analysis, we study the characteristics of solutions in two specific cases: one when ω² ≠ 0, ab and the other when ω = 0. Because polynomials in several complex variables may exhibit periodic behavior, a property that differs from polynomials in single complex variables, our study of finding solutions of equations in ℂⁿ is significant. The main results of the paper improved several known results in ℂⁿ for n ≥ 2. Additionally, the corollaries generalize results of Xu et al. [Rocky Mountain J. Math. 52(6) (2022), 2169-2187] for trinomial equations with arbitrary coefficients in ℂⁿ. Finally, we provide examples that endorse the validity of the conclusions drawn from the main results and their related remarks.

• Journal of Magnetics
• /
• 제15권4호
• /
• pp.204-208
• /
• 2010

Local wall thinning in pipelines affects the structural integrity of industries like nuclear power plants (NPPs). In the present study, a pulsed eddy current (PEC) differential probe with two excitation coils and two Hall-sensors was fabricated to measure the wall thinning in insulated pipelines. A stainless steel test sample was prepared with a thickness that varied from 1 mm to 5 mm and was laminated by plastic insulation to simulate the pipelines in NPPs. The excitation coils in the probe were driven by a rectangular current pulse, the difference of signals from two Hall-sensors was measured as the resultant PEC signal. The peak value of the detected signal is used to describe the wall thinning. The peak value increased as the thickness of the test sample increased. The results were measured at different insulation thicknesses on the sample. Results show that the differential PEC probe has the potential to detect wall thinning in an insulated NPP pipelines.