• Journal of computational fluids engineering
• /
• v.2 no.1
• /
• pp.84-92
• /
• 1997

In this paper a new structured grid generation technique is introduced. This new technique utilizes predictor-corrector approach, and is a marching scheme in the global sense as the hyperbolic scheme is. In the predictor step, one layer of grid cells is obtained by using Modified Advancing Front Method which generates a collection of quadrilateral cells simultaneously. In the corrector step, the layer of grid cells that is calculated in the predictor step is adjusted by solving Laplace equations to prevent grid lines from skewing and overlapping in highly curved configurations. It is shown that the resultant algorithm, named a MAP scheme, which combines the Modified Advancing Front Method as a Predictor with an elliptic scheme as a corrector can be used to generate globally smooth and locally near-orthogonal grids for external flow fields even for highly curved configurations. Examples of grid generations for external flow fields about several configurations by use of the present approach are given, and its applicability and flexibility have been demonstrated and discussed.

• Journal of applied mathematics & informatics
• /
• v.7 no.2
• /
• pp.483-491
• /
• 2000

In this paper, we use the auxiliary principle technique to suggest and analyze a class of predictor-corrector methods for solving noncoercive mixed variational inequalities. The convergence of the proposed method requires only the partially relaxed strongly monotonicity. which is even weaker than the co-coercivity. As special cases, we obtain a number of new and known results for classical variational inequalities.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1725-1739
• /
• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.21-25
• /
• 1998

An algorithm for a solution of ordinary differential equations using a modified corrector in the Adams predictor-corrector method of order four is described. The Lagrange interpolation used in the corrector of the Adams method is replaced partially by the cubic spline interpolation satisfying the first derivative constraints at the two end points. By exhibiting three examples, we show that the proposed method is more effcient when the solution of a differential equation is highly oscillating.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.11-27
• /
• 2003

A fourth order in time and second order in space scheme using a finite-difference method is developed for the non-linear Boussinesq equation. For the solution of the resulting non-linear system a predictor-corrector pair is proposed. The method is analyzed for local truncation error and stability. The results of a number of numerical experiments for both the single and the double-soliton waves are given.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2002.05a
• /
• pp.78-81
• /
• 2002

To achieve high precision machine totals with high speed, it is needed to develop excellent rigidity statically, dynamically and thermally as well. In this view the chief things that thermal deformation of machine tool structure is directly related to high precision. And thermal behavior for transmission procedure have an effect on high precision. It is needed to exact temperature distribution of each members and all contact elements included for machine tool structure. This paper deals with thermal behavior caused by temperature variation in a high speed feeding process. At this procedure of temperature distribution is estimated using a Predictor-Corrector Method.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.54 no.9
• /
• pp.457-460
• /
• 2005

This paper proposes a new Interior Point Method algorithm to improve the computation speed and solution stability, which have been challenging problems for employing the nonlinear Optimal Power Flow. The proposed algorithm is different from the tradition Interior Point Methods in that it adopts the Predictor-Corrector Method. It also accommodates the five minute dispatch, which is highly recommenced in modern electricity market. Finally, the efficiency and applicability of the proposed algorithm is demonstrated with a case study.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.16.2-16
• /
• 2003

미분 방정식의 수치적 해를 나타내는 방법 중 예측자-수정자 방법(predictor-corrector method)으로 알려진 Adams-Bashford-Moulton 방법은 다단계 방법을 이용하기 때문에 일단계 방법에 비하여 훨씬 좋은 수치적인 결과를 보여주고 있다. 이제, 이 다단계 방법에 오차제어 변수를 첨가한 새로운 형태의 예측자-수정자 방법을 제시하고 안정적인 해를 구할 수 있는 오차 제어 변수의 범위를 확인한다. 또한, 새로운 형태의 예측자-수정자 방법이 기존의 방법에 비하여 미분 방정식의 해에 대한 오차를 줄일 수 있는 방법임을 수치적인 결과를 통하여 검증한다.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
• /
• v.12 no.3
• /
• pp.133-141
• /
• 2007

A finite element model is developed for the extended Boussinesq equations that is capable of simulating the dynamics of long and short waves. Galerkin weighted residual method and the introduction of auxiliary variables for 3rd spatial derivative terms in the governing equations are used for the model development. The Adams-Bashforth-Moulton Predictor Corrector scheme is used as a time integration scheme for the extended Boussinesq finite element model so that the truncation error would not produce any non-physical dispersion or dissipation. This developed model is applied to the problems of solitary wave propagation. Predicted results is compared to available analytical solutions and laboratory measurements. A good agreement is observed.

• Nuclear Engineering and Technology
• /
• v.54 no.12
• /
• pp.4722-4730
• /
• 2022

This paper introduces a new point depletion-based source term calculation code named BESNA (Bateman Equation Solver for Nuclear Applications), which is aimed to estimate nuclide inventories and source terms from spent nuclear fuels. The BESNA code employs a new modified CE/CM (Constant Extrapolation - Constant Midpoint) predictor-corrector scheme in depletion calculations for improving computational efficiency. In this modified CE/CM scheme, the decay components leading to the large norm of the depletion matrix are excluded in the corrector, and hence the corrector calculation involves only the reaction components, which can be efficiently solved with the Talyor Expansion Method (TEM). The numerical test shows that the new scheme substantially reduces computing time without loss of accuracy in comparison with the conventional scheme using CRAM (Chebyshev Rational Approximation Method), especially when the substep calculations are applied. The depletion calculation and source term estimation capability of BESNA are verified and validated through several problems, where results from BESNA are compared with those calculated by other codes as well as measured data. The analysis results show the computational efficiency of the new modified scheme and the reliability of BESNA in both isotopic predictions and source term estimations.