• Title/Summary/Keyword: numerical methods

Search Result 5,244, Processing Time 0.168 seconds

THE NUMERICAL SOLUTION OF SHALLOW WATER EQUATION BY MOVING MESH METHODS

  • Shin, Suyeon;Hwang, Woonjae
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.25 no.3
    • /
    • pp.563-577
    • /
    • 2012
  • This paper presents a moving mesh method for solving the hyperbolic conservation laws. Moving mesh method consists of two independent parts: PDE evolution and mesh- redistribution. We compute numerical solution of shallow water equation by using moving mesh methods. In comparison with computations on a fixed grid, the moving mesh method appears more accurate resolution of discontinuities.

Numerical Stability of Cholesky Factorization in Interior Point Methods for Linear Programming (내부점 방법에서 촐레스키 분해의 수치적 안정성)

  • Seol, Tong-Ryeol;Seong, Myeong-Ki;Ahn, Jae-Geun;Park, Soon-Dal
    • Journal of Korean Institute of Industrial Engineers
    • /
    • v.25 no.3
    • /
    • pp.290-297
    • /
    • 1999
  • In interior point methods for linear programming, we must solve a linear system with a symmetric positive definite matrix at every iteration, and Cholesky factorization is generally used to solve it. Therefore, if Cholesky factorization is not done successfully, many iterations are needed to find the optimal solution or we can not find it. We studied methods for improving the numerical stability of Cholesky factorization and the accuracy of the solution of the linear system.

  • PDF

NUMERICAL METHODS FOR A STIFF PROBLEM ARISING FROM POPULATION DYNAMICS

  • Kim, Mi-Young
    • Korean Journal of Mathematics
    • /
    • v.13 no.2
    • /
    • pp.161-176
    • /
    • 2005
  • We consider a model of population dynamics whose mortality function is unbounded. We note that the regularity of the solution depends on the growth rate of the mortality near the maximum age. We propose Gauss-Legendre methods along the characteristics to approximate the solution when the solution is smooth enough. It is proven that the scheme is convergent at fourth-order rate in the maximum norm. We also propose discontinuous Galerkin finite element methods to approximate the solution which is not smooth enough. The stability of the method is discussed. Several numerical examples are presented.

  • PDF

A Study on Numerical Analysis of Equation of Motion for Constrained Systems (구속된 시스템 운동방정식의 수치해석에 관한 연구)

  • 은희창;정헌수
    • Journal of KSNVE
    • /
    • v.7 no.5
    • /
    • pp.773-780
    • /
    • 1997
  • Using Generalized Inverse Method presented by Udwadia and Kalaba in 1992, we can obtain equations to exactly describe the motion of constrained systems. When the differential equations are numerically integrated by any numerical integration scheme, the numerical results are generally found to veer away from satisfying constraint equations. Thus, this paper deals with the numerical integration of the differential equations describing constrained systems. Based on Baumgarte method, we propose numerical methods for reducing the errors in the satisfaction of the constraints.

  • PDF

Numerical Behavior Analysis for the Various Multiple Bolted Connections (다양한 다중 볼트 접합부의 거동에 대한 수치해석)

  • Kim, Gwang-Chul
    • Journal of the Korean Wood Science and Technology
    • /
    • v.36 no.3
    • /
    • pp.24-29
    • /
    • 2008
  • Numerical analysis model was used to analyse the behaviors of multiple bolted connections. Axial-bending element was supposed as basic model, and the effects of frame members and steel fasteners were classified for the behavior analysis. In the condition only two bolts were used, the traditional analytical methods, which show somewhat accuracy, have some advantages more than numerical analysis that need many time consuming, However, more many bolts were used in practical field condition. Also, it is impossible to analyse the behaviors of various bolts layouts and arrangements conditions by traditional analytical methods. Therefore, there is only numerical analysis method for the accurate behavioranalysis on the practical bolted connection condition. Therefore, numerical analysis method was applied on the various multiple bolted connections. On the result exactness and the reflection of connection condition, numerical analysis method showed the superiority more than widely used traditional empirical analysis methods as yield model.

Prediction of the Logitudinal Aerodynamic Coefficients of the Aircraft at Low Speed (항공기 저속 세로축 공력 계수 예측에 관한 연구)

  • Kang, Jung-Hoon
    • Journal of the Korean Society for Aviation and Aeronautics
    • /
    • v.8 no.1
    • /
    • pp.83-95
    • /
    • 2000
  • Lift, drag, pitching moment, what we call longitudinal aerodynamic coefficient, effects airplanes directly, so the method to find the accurate result quickly is an important factor from the beginning of the aircraft design. There are different ways to find aerodynamic coefficient such as empirical methods, numerical analysis methods, wind tunnel tests, and finally through an actual flight tests, but choosing the best methods depends on the due date or the cost. The accuracy varies on each design level, but all this methods have relationship to complement and balance each other, so by combining proper methods, the best result can be obtained. At this paper, empirical methods and numerical analysis method were experimented, compared, and reviewed to find the availability of each method and by combining two methods accurate result was obtained. So, we applied this methods to predict the aerodynamic coefficient on cruise configuration aircraft, and was able to obtain more accurate result on the low speed longitudinal aerodynamic coefficient. Also by watching there result, we are able to predict the errors before the actual wind tunnel test.

  • PDF

A Case Study on Team Project in Calculus for Medicine - Numerical Methods of Integration - (의대생을 위한 미분적분학 팀프로젝트 사례 - 정적분의 수치채산법을 중심으로 -)

  • Min, Sook
    • Communications of Mathematical Education
    • /
    • v.26 no.2
    • /
    • pp.155-176
    • /
    • 2012
  • In this paper, we present a practical and essential method of using team projects for calculus. We, specifically, take into account the team project that calculate the volume of lung represented on CT scan images. We have demonstrated that the process of analyzing the images in a team project encourage studying numerical methods of integration for calculus. Also, we have used various technological programs(MATLAB, MATHEMATICA, MS Excel) to solve the team project.

A Study on the Influence of Ground Subsidence and Stability of Buildings by Tunnel Excavation in Urban Area using Numerical Analysis and Neural Network Method (수치해석 및 인공신경망 기법을 이용한 도심지 터널 굴착에 의한 침하영향 및 연도변 건물 안정성 평가)

  • Park, Sung-Ryong;Kim, Eun-Kyum;Sa, Gong-Myung
    • Proceedings of the KSR Conference
    • /
    • 2007.11a
    • /
    • pp.585-594
    • /
    • 2007
  • This paper presents the methods which estimate the influence of ground subsidence and the stability of buildings by tunnel excavation in urban area. First, we study the behaviour of ground subsidence using neural network and numerical method. And we analyze the characteristic of both methods. Using the both methods, we evaluate the stability of buildings by subway tunnel excavation and we compare the results of the neural network and numerical analysis.

  • PDF

COMBINED LAPLACE TRANSFORM WITH ANALYTICAL METHODS FOR SOLVING VOLTERRA INTEGRAL EQUATIONS WITH A CONVOLUTION KERNEL

  • AL-SAAR, FAWZIAH M.;GHADLE, KIRTIWANT P.
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.22 no.2
    • /
    • pp.125-136
    • /
    • 2018
  • In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.

Study on Numerical Method for Combustion-Gas Flow Field of Granular Type Solid Propellant (과립형 고체추진제의 연소가스 유동장 해석을 위한 수치해석 기법 연구)

  • Sung, Hyung-Gun;Jang, Jin-Sung;Roh, Tae-Seong;Choi, Dong-Whan
    • 한국전산유체공학회:학술대회논문집
    • /
    • 2008.03b
    • /
    • pp.551-554
    • /
    • 2008
  • In this study, numerical methods for the code development of the interior ballistics have been conducted. Mathematical models and numerical methods for the analysis technique of the granular solid propellants have been investigated. As the results of applying the methods of errors have been generated by calculation for the specific surface area of the granular solid propellants. To remove these error, the developed Eulerian-Larangian method for multiphase flows has been suggested.

  • PDF