• 융합보안논문지
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• 제5권3호
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• pp.93-97
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• 2005

MacCormack 방법은 hyperbolic 편미분 방정식의 근을 구하는데 많이 쓰이는 방법으로 그 정확도가 2차 오더가 된다. 하지만 이 방법으로 편미분방정식을 풀 경우 불연속인 점에서는 엔트로피를 만족하지 않는 경우가 있어 우리는 임의의 항을 첨가하여 근을 구해야한다. 이 임의의 항을 첨가하지 않고 직접 방정식으로부터 구하는 방법을 생각하는데 있어서 기존의 MacCormack 방법에 새 central scheme의 개념을 이용하면 전형적인 MacCormack 방법의 정확도와 장점을 보존할 수 있다. 이 새로운 방법을 이용하여 1D Burgers' 방정식과 1D Euler gas dynamic 방정식에 활용하여 그 결과를 살펴본다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.83-102
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• 2015

The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge-Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.

• Steel and Composite Structures
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• 제2권3호
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• pp.195-208
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• 2002

Elasticity solutions to the boundary-value problems of dynamic response under transverse asymmetric load of cross-ply shallow cylindrical panels are presented. The shell panel is simply supported along all four sides and has finite length. The highly coupled partial differential equations are reduced to ordinary differential equations with constant coefficients by means of trigonometric function expansion in the circumferential and axial directions. The resulting ordinary differential equations are solved by Galerkin finite element method. Numerical examples are presented for two (0/90 deg.) and three (0/90/0 deg.) laminations under dynamic loading.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Structural Engineering and Mechanics
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• 제75권3호
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• pp.357-367
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• 2020

The objective of this article is investigation of dynamic response of thick multilayer functionally graded (FG) beam under generalized dynamic forces. The plane stress problem is exploited to describe the constitutive equation of thick FG beam to get realistic and accurate response. Applied dynamic forces are assumed to be sinusoidal harmonic, sinusoidal pulse or triangle in time domain and point load. Equations of motion of deep FG beam are derived based on the Hamilton principle from kinematic relations and constitutive equations of plane stress problem. The numerical finite element procedure is adopted to discretize the space domain of structure and transform partial differential equations of motion to ordinary differential equations in time domain. Numerical time integration method is used to solve the system of equations in time domain and find the time responses. Numerical parametric studies are performed to illustrate effects of force type, graduation parameter, geometrical and stacking sequence of layers on the time response of deep multilayer FG beams.

• International Journal of Aeronautical and Space Sciences
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• 제18권4호
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• pp.816-826
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• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.312-315
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• 1993

Optimal control theories based on the maximum principles have been evolved and applied to distributed parameter systems(DPSs) represented by partial differential equations (PDEs) and integral equations (IEs). This paper intends to show that an optimal control of a tubular reactor described by a one-dimensional partial differential equation was obtained using the distributed parameter control method for parabolic PDEs. In develping an algorithm which implements the calculation, the method of lines (MOL) was adopted through using a package called the DSS/2. For the tubular reactor system chosen for this paper, the optimal control method based on PDEs with the numerical MOL showed to be more efficient than the one based on IEs.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.281-294
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• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• 충청수학회지
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• 제26권3호
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• pp.501-516
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• 2013

The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall's inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.

• 한국컴퓨터산업학회논문지
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• 제7권1호
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• pp.33-38
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• 2006

케이블 뿐 아니라 현수교의 운동은 비선형 미분방정식에 지배된다. 미분방정식은 비선형성 때문에 진폭이 큰 해가 존재한다. 유한차분법을 이용하여 비선형 방정식의 주기근을 구한다. 일노드의 힘과 힘의 약간 변형된 형태를 이용하여 방정식의 해를 구한다.