带显式级的A-稳定的对角隐式龙格-库塔方法  

A-stable Diagonally-Implicit Runge-Kutta Methods with an Explicit Stage

作　　者：李聪颖[1] 

机构地区：[1]怀化学院数学系,湖南怀化418008

出　　处：《怀化学院学报》2010年第2期23-28,共6页Journal of Huaihua University

摘　　要：证明了A-稳定的级阶不低于2的3级对角隐式Runge-Kutta方法的阶至多为3;构造了级阶为2、有显式级的A-稳定的三级三阶对角隐式Runge-Kutta公式双参数簇.所构造的方法簇适于求解刚性微分方程初值问题.This article maintains that the order of A - stable three - stage diagonally - implicit Runge - Kutta methods of stage - order two is no more than three is proved. A two - parameter family of three - stage diagonally - implicit Runge - Kutta methods of order three and stage - order two are constructed, and this family have an explicit stage. The constructed methods are efficient for solving the initial value problems of stiff differential equations.

关 键 词：刚性微分方程 对角隐式Runge—Kutta方法 A-稳定性 L-稳定性 级阶 

分 类 号：O175[理学—数学]