三角形域上边界型积分公式的误差估计

Error Estimations of Boundary-Type integration Formulas on a Triangle

本文对三角形域上边界型近似积分公式首次给出精确的误差渐近估计,并由此建立相应的Romberg型外推公式.同时,讨论了若干数值应用,包括提出一种新的求解Volterra型积分微分方程初值问题的数值方法.

In this paper,some sophisticated error estimations of the boundary-type integration formulas on a triangle are obtained.Based on that,a seriesof compounded formulas in the form of Romberg's extrapolation are derived.Several numerical applications,including a new method to solve Volterratype of integro-differential equations,are also given.