상미분방정식의 시간일치 수치해법과 안정성

Abstract

Nowadays, the numerical time integration schemes are mainly used in the research of hydrodynamic problems. And the application has become widened more and more. However, the study of the numerical scheme in the view point of accuracy and stability seldom has been done recently, on the contrary many studies in former days. Without accuracy and stability check of numerical scheme, the conclusion on the calculations of delicate hydrodynamic problem may be misled. In this paper, the Time-Consistent numerical method for ordinary differential equation was introduced. This method has error of O(h^2) in time and error of O(h^3) in update equation. The numerical stability was investigated, the method introduced in this paper is proven to be more stable than the other one-step numerical methods.