基于埃尔米特插值的隐式线性多步法公式

为求解常微分方程数值解,文中运用数值积分法,采用埃尔米特插值多项式,推导出三个等距节点的六阶隐式线性多步法公式;并且对所建立公式的精度进行了分析;进一步通过实例运用计算机编程将阿达姆斯外推法等线性多步法和所建立的公式进行了精度比较。结果证明,所建立的隐式线性多步法公式比现有的具有相同节点的线性多步法公式精度更高,求解速度更快,有一定的应用价值。

Implicit Linear Multistep Formula Based on Hermite Interpolation

In order to obtain the numerical solution of ordinary differential equation,this paper utilized the numerical integration,and used Hermite Interpolation,infered a sixth order implicit linear multistep formula on three equal-spaces pitch points.And the formula precision which established was analyzed;Furthermore,through the example of computer programming,comparision of the formula precision which established Ang Adams extrapolation linear multistep method was made.The result proved the precision of implicit linear multistep formula just established was still higher and quicker than the existing formula bearing the same pitch point in solution speed.Thus the established implicit linear mulfistep method values to a certain extent in application.