一类精确指数拟合的Runge-Kutta方法

摘要

构造了一类含自由参数ω≠0的精确指数拟合的一级Runge-Kutta方法,若ω→0,当c1=0,这类方法是显示的单步Euler方法,是一阶收敛的;当c1=1/2,这类方法是隐式的中点公式,是二阶收敛的;当c1=1,这类方法是隐式的向后Euler方法,是一阶收敛的.它们都是L-稳定的.根据估计局部截断误差,给出了自动控制步长选择最优参数ω的算法,并给出数值算例证明所提出方法的优越性.%A class of exponential fitted Runge-Kutta method with a free parameter to #0is constructed. If ω→ 0,when cI =0 the method is explicit one step Euler method with first order convergence; when cl = 1/2 the method is implicit midpoint formula and of second order convergence; when c1 = lthe method is implicit back- ward Euler method and of first order convergence. Both of them areL-stable. Based on the estimation of local truncation error, an automatic step size control algorithm is given to choose the optimal parametertosuch that the error is as small as possible. Numerical tests are shown so as to support the superiority of the proposed method.