• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.697-726
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• 1999

In this paper we develop a now procedure to control stepsize for linear multistep methods applied to semi-explicit index 1 differential-algebraic equations. in contrast to the standard approach the error control mechanism presented here is based on monitoring and contolling both the local and global errors of multistep formulas. As a result such methods with the local-global stepsize control solve differential-algebraic equation with any prescribed accuracy (up to round-off errors). For implicit multistep methods we give the minimum number of both full and modified Newton iterations allowing the iterative approxima-tions to be correctly used in the procedure of the local-global stepsize control. We also discuss validity of simple iterations for high accuracy solving differential-algebraic equations. Numerical tests support the the-oretical results of the paper.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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• pp.179-202
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• 2019

This paper presents second derivative generalized extended backward differentiation formulas (SDGEBDFs) based on the second derivative linear multi-step formulas of Cash [1]. This class of second derivative linear multistep formulas is implemented as boundary value methods on stiff problems. The order, error constant and the linear stability properties of the new methods are discussed.

• 한국전산유체공학회지
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• 제7권4호
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• pp.35-41
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• 2002

The projectile afterbodies for zero-lift drag reduction has been analyzed using the Navier-Stokes equations with the κ-εturbidence model. The numerical method of a second order upwind scheme has been used on an unstructured adaptive grid system. Base drag reduction methods that have been found effective on axisymmetric bodies are boattailing, base bleed, base combustion, locked vortex afterbodies and multistep afterbodies. In this paper, turbulence flow and pressure charateristics have been studied for geometries of multistep afterbodies. The important geometrical and flow parameters relevant to the design of such afterbodies have been identified by step number, length and height. The flow over multistep aftoerbodies or base have many kinds of compressible flow characteristics including expansion waves at the trailing edge, recompression waves, separation and recirculating flow in the base region, shear flow and wake flow. The numerical results have been compared and analyzed with the experimental data. The flow characteristics have been clearly shown.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2001년도 춘계 학술대회논문집
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• pp.60-65
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• 2001

The projectile afterbodies for zero-lift drag reduction has been analyzed using the Navier-Stokes equations with the $\kappa-\epsilon$ turbulence model. The numerical method of a second order upwind scheme has been used on unstructured adaptive meshes. Base drag reduction methods that have been found effective on axisymmetric bodies include boattailing, base bleed, base comustion, locked vortex afterbodies and multistep afterbodies. In this paper, the charateristics of turbulence flow have been studied for geomeries of multistep afterbodies. The important geometrical and flow parameters relevant to the design of such afterbodies have been identified by number, length and height of step. The flow over multistep afterbodies has been analyzed including expansion waves, recompression waves, recirculating flow, shear flow and wake flow. The numerical results have been compared and analyzed with the experimental datum.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권3호
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• pp.243-291
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• 2020

In this paper, multi-block generalized backward differentiation methods for numerical solutions of ordinary differential and differential algebraic equations are introduced. This class of linear multi-block methods is implemented as multi-block boundary value methods (MB₂ VMs). The root distribution of the stability polynomial of the new class of methods are determined using the Wiener-Hopf factorization of a matrix polynomial for the purpose of their correct implementation. Numerical tests, showing the potential of such methods for output of multi-block of solutions of the ordinary differential equations in the new approach are also reported herein. The methods which output multi-block of solutions of the ordinary differential equations on application, are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output only a block of solutions per step. The MB₂ VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.

• 한국터널지하공간학회 논문집
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• 제12권5호
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• pp.359-368
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• 2010

국내의 경우 터널 지반보강증 강관다단그라우팅 공법이 폭넓게 시용되지만 해외의 경우 시공성 및 경제성이 막장볼트 공법이 흔히 적용되고 있다. 본 논문에서는 국내 도로터널 붕락 발생시 적용한 강관다단그라우팅 및 막장볼트의 적용효과에 대해서 수치해석을 통해 분석해 보았다. 또한 해외 시공사례의 계측데이터를 바탕으로 두 공법의 보강효과에 대해 분석해 보았다. 본 연구를 통해 막장 전면에 파쇄대가 발달하는 경우 페이스공법도 막장보강에 효과적임을 알 수 있었다.

• 대한기계학회논문집B
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• 제27권4호
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• pp.458-465
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• 2003

The main objective of the research is to develop a research code solving transient incompressible Navier-Stokes equation. In this research code, Adams-Bashforth method was applied to the convective terms of the navier stokes equation and the splitted equations were discretized spatially by finite element methods to solve the complex geometry problems easily. To reduce the divergence on the boundaries of pressure poisson equation due to the unsuitable pressure boundary conditions, multi step approximation pressure boundary conditions derived from the boundary linear momentum equations were used. Simulations of Lid Driven Flow and Flow over Cylinder were conducted to prove the accuracy by means of the comparison with results of the previous workers.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• 천문학논총
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• 제8권1호
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• pp.137-151
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• 1993

We have calculated the astronomical almanac 1994 and simulated the trajectory of a satellite orbit considering all perturbative forces with various initial conditions. In this work, Gauss Jackson multistep integration method has been used to calculate our basic equation of motion with high numerical accuracy. It has beer. found that our results agree well with the Astronomical Almanac Data distributed by JPL of NASA and the orbit simulations have been carried out with fast speed, stability and excellent round-off error accumulation, comparing with other numerical methods. In order to be carried out our works on almanac and orbit calculations easily by anyone who uses a personal computer, we have made a computer program on graphical user interface to provide various menus for detail works selected by a mouse.