二重数值积分公式的高精度对偶公式及其应用

摘要

给出了计算二重积分的Simpson公式与两点高斯公式的对偶公式的构造过程,得到与之对应的高精度对偶修正解,提高了二重数值积分公式的计算精度,同时给出了二重积分的一种估值方法.最后,应用于几个典型的数值算例,计算结果表明：对偶修正解比对应的数值积分公式及其对偶公式的解有更高的计算精度和更快的收敛速度.%The dual schemes of Simpson and two-point Gauss numerical integration formulae are constructed,and high order accurate dual modified solutions are obtained.These dual modified solutions improve computational accuracy of double numerical integration formulae.Moreover,they present a kind of method of estimated double integration value.Finally,several typical numerical experiments are given.Numerical results show that dual modified solutions have the higher computational accuracy and faster convergence rate than that of the corresponding numerical integration formulae and theirs dual solutions.