• Water Engineering Research
• /
• 제2권3호
• /
• pp.187-196
• /
• 2001

An approximate analytical solution of a nonlinear hydro-thermo coupled diffusion equation is derived using the dimensionless form of the equation and transformation method. To derive an analytical solution, it is drastically assumed that the product of first order derivatives in the non-dimensionalized governing equation has little influence on the solution of heat and moisture behavior problem. The validity of this drastic assumption is demonstrated. Some numerical simulation is performed to investigate the applicability of a derived approximate analytical solution. The results show a good agreement between analytical and numerical solutions. The proposed solution may provide a useful tool in the verification process of the numerical models. Also, the solution can be used for the analysis of one-dimensional coupled heat and moisture movements in unsaturated porous media.

• 한국전산응용수학회:학술대회논문집
• /
• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
• /
• pp.4.2-4
• /
• 2003

In this paper, we describe how to approximate the solutions of partial differential equations by bicubic spline functions whose interpolation errors at non-grid points are smaller in general than those by linear interpolations of the original solution at grid points. We show that the bicubic spline function can be represented exactly or approximately by a fuzzy system, and that the resulting fuzzy rule table shows the contours of the solution function. Thus, the fuzzy rule table is identified as a digital image and the contours in the rule table provide approximate contours of the solution of partial differential equations. Several illustrative examples are included.

• 대한수학회지
• /
• 제52권2호
• /
• pp.349-372
• /
• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

• 한국연소학회지
• /
• 제7권3호
• /
• pp.37-46
• /
• 2002

Characteristics of lifted flames in axisymmetric laminar coflow jets have been investigated experimentally. Approximate solutions for velocity and concentration accounting virtual origins have been proposed for coflow jets to analyze the behavior of liftoff height. From the measurement of Rayleigh intensity for probing the concentration field of propane, the validity of the approximate solutions was substantiated. From the images of OH PLIF and CH chemiluminescence and the Rayleigh concentration measurement, it has been shown that the positions of maximum luminosity in direct photography coincide with the tribrachial points, which were located along the stoichiometric contour. The liftoff height in coflow jets was found to increase highly nonlinearly with jet velocity and was sensitive to coflow velocity.

• 한국생산제조학회지
• /
• 제24권2호
• /
• pp.192-197
• /
• 2015

In many fields, the importance of reducing weight is increasing. A product should be designed such that it is profitable, by lowering costs and exhibiting better performance than other similar products. In this study, the mass and deflection of steel structures have to be reduced as objective functions under constraint conditions. To reduce computational analysis time, central composite design(CCD) and D-Optimal are used in design of experiments(DOE). The accuracy of approximate models is evaluated using the $R^2$ value. In this study, the objective functions are multiple, so the non-dominant sorting genetic algorithm(NSGA-II), which is highly efficient, is used for such a problem. In order to verify the validity of Pareto solutions, CAE results and Pareto solutions are compared.

• Structural Engineering and Mechanics
• /
• 제50권6호
• /
• pp.853-862
• /
• 2014

In this paper, two approximate analytical methods have been applied to forced nonlinear vibration problems to assess a high accurate analytical solution. Variational Iteration Method (VIM) and Perturbation Method (PM) are proposed and their applications are presented. The main objective of this paper is to introduce an alternative method, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Some patterns are illustrated and compared with numerical solutions to show their accuracy. The results show the proposed methods are very efficient and simple and also very accurate for solving nonlinear vibration equations.

• 설비공학논문집
• /
• 제17권4호
• /
• pp.303-311
• /
• 2005

The problem of conjugate laminar film condensation of the pure saturated vapor in forced flow over a flat plate has been investigated as boundary layer solutions. A simple and efficient numerical method is proposed for its solution. The interfacial temperature is obtained as a root of 3rd order polynomial for laminar film condensation, and it is presented as a function of the conjugate parameter. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Jacob number, $Ja^{\ast}$, defined by an overall temperature difference, a property ratio R and the conjugate parameter ${\zeta}$. The approximate solutions thus obtained reveal the effects of the conjugate parameter.

• 대한화학회지
• /
• 제53권6호
• /
• pp.663-670
• /
• 2009

논랜덤 혼합의 2-성분 격자용액에서 특정상호작용을 갖는 경우의 수에 대한 분포를 난수 모의실험을 통하여 구하였다. 이 분포로부터 2-성분격자용액의 과잉깁스에너지 $G^E$에 대한 근사식을 유도하였다. 이 식을 사용하여 15개의 2-성분용액에 대한 일정압력에서의 액체-증기 상평형 계산을 하였고 Wilson식, Van Laar식, Redlich-Kister식의 계산 결과와 비교하여 보았다.

• Wind and Structures
• /
• 제21권3호
• /
• pp.273-287
• /
• 2015

In this paper, a free vibration analysis of functionally graded beam made of porous material is presented. The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Nonlinear Functional Analysis and Applications
• /
• 제26권3호
• /
• pp.497-512
• /
• 2021

In this paper, we study the analytical and approximate solutions for a fractional quadratic integral equation involving Katugampola fractional integral operator. The existence and uniqueness results obtained in the given arrangement are not only new but also yield some new particular results corresponding to special values of the parameters 𝜌 and ϑ. The main results are obtained by using Banach fixed point theorem, Picard Method, and Adomian decomposition method. An illustrative example is given to justify the main results.