一类三级对角隐式Runge-Kutta方法的阶与稳定性分析  

Order and Stability Analysis for a Class of Three-stage Diagonally-implicit Runge-Kutta Method

作　　者：陈全发[1] 李聪颖[2] 

机构地区：[1]湘南学院数学系,郴州423000 [2]怀化学院数学系,怀化418000

出　　处：《工程数学学报》2009年第4期703-710,共8页Chinese Journal of Engineering Mathematics

基　　金：湖南省高等教育科研资助课题(08C825)

摘　　要：基于经典Runge-Kutta方法,本文建立了一类含一个自由参数、阶数不小于4且级阶不小于2的三级对角隐式Runge-Kutta公式,讨论了该公式的阶条件和阶结果。构造了级阶为2的三级3阶对角隐式Runge-Kutta公式,证明了A-稳定的级阶不小于2的三级对角隐式Runge-Kutta公式的阶至多为3。利用稳定函数,在约定条件下,证明了所构造的Runge-Kutta公式的A-稳定性、L-稳定性和代数稳定性。随后的数值实验中,验证了理论的正确性和算法的有效性。Based on the classical Runge-Kutta algorithm, this paper constructed a kind of three-stage diagonally-implicit Runge-Kutta formula including a free parameter, with the order no less than four, and the stage order no less than two. We discussed the order condition and the result for this formula. The three-stage diagonally-implicit Runge-Kutta method of three order and two stages order was then established. It was proved that the order of A-stable three-stage diagonally-implicit Runge-Kutta method with stages order more than two was no more than three. Using stability function and the condition of agreement, the paper proved the A-stability, the L-stability and the algebra stability for the established Runge-Kutta formula. Numerical experiments were presented to verify the theoretical results.

关 键 词：对角隐式 Runge—Kutta方法 阶 稳定性 

分 类 号：O241.81[理学—计算数学]