解二阶常微分方程y″=g(x,y)初值问题的含参数线性多步方法

Linear multistep methods with a parameter for solving initial value problems of second order ordinary differential equations y″=g(x,y)

对二阶常微分方程y″=g(x ,y)的初值问题 ,给出了k步k阶显式和k步k +1阶隐式含参数线性多步方法 ,当任意正整数k≥ 2时 ,这两类方法都是P 稳定的 .数值试验表明 ,由这两类同阶方法所构成的PECE格式是十分有效的 .

For initial value problems of second ordinary differential equations y″=g(x,y),the paper presents implicit k-step (k+1) order and explicit k-step k order linear multistep methods with a parameter for any positive integer k≥2,respectively. They are all P-stable. Numerical tests show that the PECE schemes formed by the explicit and implicit the same order formulae are efficient.