• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.479-483
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• 2006

For any fixed $\lambda\leq-\frac{1}{2}$, there exists $f(\eta){\in}C^1[0,+\infty)$ which satisfies the following nonlinear boundary value problem f'+ff'+$\lambda(l-f'^2)=0$ a.e.in $(0,+\infty)$, f(0)=0, f'(0) = 0, $f'(+\infty)=1$, which arises in boundary layer theory in fluid mechanics.

• International Journal of High-Rise Buildings
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• v.11 no.4
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• pp.331-346
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• 2022

Reproducing the horizontally homogeneous atmospheric boundary layer in computational wind engineering is essential for predicting the wind loads on structures. One of the important issues is to use fully developed inflow conditions, which will lead to the consistence problem between inflow condition and internal roughness. Thus, by analyzing the previous results of computational fluid dynamic modeling turbulent horizontally homogeneous atmospheric boundary layer, we modify the past hypotheses, detailly derive a new type of inflow condition for standard k-ε turbulence model. A group of remedial approaches including formulation for wall shear stress and fixing the values of turbulent kinetic energy and turbulent dissipation rate in first wall adjacent layer cells, are also derived to realize the consistence of inflow condition and internal roughness. By combing the approaches with four different sets of inflow conditions, the well-maintained atmospheric boundary layer flow verifies the feasibility and capability of the proposed inflow conditions and remedial approaches.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.237-250
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• 1995

A hopf bifurcation of a free boundary (or an internal layer) occurs in solidification, chemical reactions and combustion. It is a well-known fact that a free boundary usually appear as sharp transitions with narrow width between two materials ([2]).

• Earthquakes and Structures
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• v.9 no.1
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• pp.173-194
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• 2015

Site response analysis is an important topic in earthquake engineering. A time-domain numerical method called as one-dimensional (1D) finite element artificial boundary method is proposed to simulate the homogeneous plane elastic wave propagation in a layered half space subjected to the obliquely incident plane body wave. In this method, an exact artificial boundary condition combining the absorbing boundary condition with the inputting boundary condition is developed to model the wave absorption and input effects of the truncated half space under layer system. The spatially two-dimensional (2D) problem consisting of the layer system with the artificial boundary condition is transformed equivalently into a 1D one along the vertical direction according to Snell's law. The resulting 1D problem is solved by the finite element method with a new explicit time integration algorithm. The 1D finite element artificial boundary method is verified by analyzing two engineering sites in time domain and by comparing with the frequency-domain transfer matrix method with fast Fourier transform.

• Bulletin of the Korean Space Science Society
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• 2004.10b
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• pp.328-331
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• 2004

Shock wave boundary layer interactions can make flows around a vehicle be very high pressure and temperature due to pass shock waves in small areas of the hypersonic vehicle. These phenomena can affect a critical problem in the design of hypersonic vehicles. To research the effect of shock wave boundary layer interactions, comer flows were studied in this paper using numerical studies with the NSMB (Navier-Stokes Multi Block) solver and then comparing corresponding numerical results with experimental data of the Huston High Speed Flow Field Workshop II. The mach number of flows is 12.3 in comer flows. The comparison with the computational result is presented based on diverse numerical schemes. Good agreement is obtained.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.99-115
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• 2022

The problem of Benard double diffusive Marangoni convection is investigated in a horizontally infinite composite layer system consisting of a two component fluid layer above a porous layer saturated with the same fluid, using Darcy-Brinkman model with constant heat sources/sink in both the layers. The lower boundary of the porous region is rigid and upper boundary of the fluid region is free with Marangoni effects. The system of ordinary differential equations obtained after normal mode analysis is solved in closed form for the eigenvalue, thermal Marangoni number for two types of thermal boundary combinations, Type (I) Adiabatic-Adiabatic and Type (II) Adiabatic -Isothermal. The corresponding two thermal Marangoni numbers are obtained and the essence of the different parameters on non-Darcy-Benard double diffusive Marangoni convection are investigated in detail.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.183-198
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• 2003

We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.487-508
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• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.