http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
A QUADRATICALLY CONVERGENT ITERATIVE METHOD FOR NONLINEAR EQUATIONS
윤병인,Miodrag S. Petkovic 대한수학회 2011 대한수학회지 Vol.48 No.3
In this paper we propose a simple iterative method for nding a root of a nonlinear equation. It is shown that the new method, which does not require any derivatives, has a quadratic convergence order. In addition, one can nd that a hybrid method combined with the non-iterative method can further improve the convergence rate. To show the efficiency of the presented method we give some numerical examples.
EVALUATION OF SINGULAR INTEGRALS BY HYPERBOLIC TANGENT BASED TRANSFORMATIONS
윤병인 대한수학회 2011 대한수학회지 Vol.48 No.1
We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.
AN IMPROVED IMPLICIT EULER METHOD FOR SOLVING INITIAL VALUE PROBLEMS
윤병인 한국산업응용수학회 2022 Journal of the Korean Society for Industrial and A Vol.26 No.3
To solve the initial value problem we present a new single-step implicit method based on the Euler method. We prove that the proposed method has convergence order 2. In practice, numerical results of the proposed method for some selected examples show an error tendency similar to the second-order Taylor method. It can also be found that this method is useful for stiff initial value problems, even when a small number of nodes are used. In addition, we extend the proposed method by using weighted averages with a parameter and show that its convergence order becomes 2 for the parameter near 21 . Moreover, it can be seen that the extended method with properly selected values of the parameter improves the approximation error more significantly.
Numerical Evaluation of Cauchy Principal Value Integrals using a Parametric Rational Transformation
윤병인 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.4
For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.