• Communications of the Korean Mathematical Society
• /
• v.4 no.1
• /
• pp.167-172
• /
• 1989

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.26 no.4
• /
• pp.353-361
• /
• 2022

For an initial value problem, using a weighted average between two adjacent approximates, we propose a simple one-step method based on the Euler method. This method is useful for solving stiff initial value problem, even when the step size is not very small. Moreover, it can be seen that the proposed method with some selected weights results in improved approximation errors.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.2
• /
• pp.433-442
• /
• 1995

For the line search of a multi-variable optimization, an efficient algorithm is presented. The algorithm sequentially employs several polynomial approximations such as 2-point quadratic interpolation, 3-point cubic interpolation/extrapolation and 4-point cubic interpolation/extrapolation. The order of polynomial function is automatically increased for improving the accuracy of approximation. The method of approximation (interpolation or extrapolation) is automatically switched by checking the slope information of the sample points. Also, for selecting the initial step length along the descent vector, a new approach is presented. The performance of the proposed method is examined by solving typical test problems such as mathematical problems, mechanical design problems and dynamic response problems.

• Communications of the Korean Mathematical Society
• /
• v.29 no.4
• /
• pp.505-518
• /
• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Journal of the Korean Institute of Telematics and Electronics A
• /
• v.31A no.10
• /
• pp.48-53
• /
• 1994

The problem of a plane wave impinging upon a semi-infinite paralle-plate waveguide is investigated. The interior fields can be analyzed by converting the initial field into vaveguide modes. Kirchhoff approximation is usually made at the waveguide aperture in the literature. In this paper, a modified approximation is made using the Uniform Gemetrical Theory of Diffraction(UTD). Numerical results show excellent agreement between UTD-supplemented mode-matching solution and UTD solution.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.575-584
• /
• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1995.04b
• /
• pp.198-203
• /
• 1995

In the paper, we have proposed a new technique to detemine the initial billet for the forged products using a function approximation in neural network. A three-layer neural network is used and a back propagation algorithm is employed totrain the network. An optimal billet which satisfied the forming limitation, minimum of incomplete filling in the die cavity, load and energyas well as more uniform distribution of effective strain, is determined by applying the ability of function approximation of te neural network. The amount of incomplete filling in the die, load and forming energyas well as effective strain are measured by the rigid-plastic finite element method. The new technique is applied tofind the optimal billet size for the axisymmetric rib-web product in hot forging. This would reduce the number of finite element simulation for determing the optimal billet of forging products, further it is usefully adapted to physical modeling for the forging design.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.04a
• /
• pp.335-342
• /
• 2001

In this paper, an improved Element-Free Galerkin (EFG) method is proposed by adding enrichment function to the standard EFG approximation and a discontinuity function is implemented in constructing the shape function across the crack surface. In this method, the singularity and the discontinuity of the crack are efficiently modeled by using initial node distribution to evaluate reliable stress intensity factor, though the standard EFG method requires placing additional nodes near the crack tip. The proposed method enables the initial node distribution to be kept without any additional nodal d.o.f. and expresses the asymptotic stress field near the crack tip successfully. Numerical example verifies the improvement and the effectiveness of the method.

• Korean Journal of Computational Design and Engineering
• /
• v.11 no.1
• /
• pp.1-10
• /
• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• Journal of applied mathematics & informatics
• /
• v.42 no.5
• /
• pp.1195-1210
• /
• 2024

This research aims to determine an optimal (best) solution for transporting the logistics at a minimum cost from various sources to various destinations. We proposed a new algorithm for the initial basic feasible solution (IBFS). Developing a new IBFS is the first step towards finding the optimal solution. A new approach for the initial basic feasible solution that reduces iterations and produces the best answer in the initial process of the transportation issue. Different IBFS approaches have been generated in the literature review. Some statistical fundamentals, such as normal distribution and the root mean square technique, are employed to find new IBFS. A TP is transformed into a normal distribution, and penalties are determined using the root mean square method. Excel Solver is used to calculate normal distribution values. The second step involves using a stepping-stone approach to compute the optimum solution. The results of our study were calculated using numerical examples and contrasted with a few other methodologies, such as Vogel's approximation, the Continuous Allocation Method (CAM), the Supply Demand Repair Method (SDRM), and the Karagul-Sahin Approximation Method (KSAM). The conclusion of our proposed method gives more accurate results than the existing approach.