中文摘要：

在这份报纸，我们设计并且分析到二维的海维赛德的数字方法工作的高顺序的一个班积分。由我们的高顺序启发了数字方法到二维的三角洲功能积分[19 ] ，方法包括接近海维赛德的网孔房间限制工作积分。在每个网孔房间，二维的海维赛德功能积分能与是的被积函数作为一维的平常的积分被重写在不可分的间隔的几个子集上光滑的一维的海维赛德功能积分。因此，二维的海维赛德功能积分被使用数字照和高度订数字方法到一维的海维赛德功能积分的标准一维的高顺序接近。我们为证明方法能由把相应精确性分到亚算法完成任何需要的精确性的方法建立错误估计。数字例子被举证明第二完成或超过期望的精确性到在这份报纸实现的第四顺序的方法。[从作者抽象]

英文摘要：

In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimen- sional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function inte- gral is approximated by applying standard one dimensional high order numerical quadra- tures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the in this paper achieve or exceed the expected second to fourth-order methods implemented accuracy.