【摘要】 在Butcher根树理论基础上引入Runge-Kutta方法的阶条件,并通过误差常数极小化技术得到一个新的4阶方法。数值实验结果表明,新方法与现有文献中的几个高效方法相比,在计算精度及效率上具有明显的优越性。更多还原

【Abstract】 The order conditions for Runge-Kutta methods are presented based on Butcher′s rooted tree theory.A new Runge-Kutta method is obtained by means of minimizing the error constant.The results of numerical experiments show the competence of the new method in accuracy and efficiency when they are compared with some highly efficient codes in the literature.更多还原