常微分方程中的隐式混合单步连续块方法(英文)

Continuous block implicit hybrid one-step methods for ODEs

推广了相关文献中用一类k-维隐式混合块方法求解微分方程初值,得到离散的数值近似解.对这些离散的数值解做连续化延伸,发现2k+2阶隐式混合单步连续块方法存在且惟一.同时还讨论了这类连续块方法在常微分方程中的A-稳定性及一些相关性质.

A class of k-block implicit hybrid methods for solving the initial value problem for ordinary differential equations（ODEs） are generalized.A continuous extension for the discrete approximate solution of ODEs generated by the block implicit hybrid methods is presented.Existence and uniqueness for the continuous methods of order 2k＋2 are studied.The A-stability and some properties of the continuous block implicit hybrid methods for ODEs are discussed.