不对等剖分的二重积分数值解法

UNEQUILATERAL DUAL DIVIDING IN NUMERICAL COMPUTATION TO DOUBLE INTEGRAL

本文以一维传统的数值积分法为基础,总结归纳出求二重积分近似值的复化梯形法、复化抛物线法的求积公式,并证明了它们的收敛性。在给出x、y两方向对等剖分的复化梯形、复化抛物线法的计算机算法和计算实例的分析之后,又进行新的探索和改进,总结出x、y两方向不对等剖分的复化梯形、复化抛物线法及其计算机算法,并得出了满意的计算实例的结果。

Based on the traditional methods of numerical integeration, this paper gives the quadratures of the duplicated trapezium rule and the duplicated Simpson's rule for solving double integral,and proves their convergence .The algorithms of the two rules by duplicated dividing have been introduced along -with two axis directions, not only equilaterally, but unequilaterally. After analysing the results of some characteristic, samples with the help of computer, we have concluded that the methods of duplicated trapezium and Simpsons' should be realized in general along with two axis directions unequilaterally.