点电荷相互作用能与一类二重积分的算法

Energy interaction and algorithms of a kind of double integration with poles

在柱面坐标系下，点电荷的相互作用能是ｚ和ρ的具有极点的二重积分。此类积分有简单的解析解，但不容易数值计算。Ｍａｔｈｅｍａｔｉｃａ３．０和ＭａｐｌｅＶ不能求解此类积分；Ｇａｕｓｓ－Ｌｅｇｅｎｄｒｅ算法只能获得粗略结果，Ｒｕｎｇｅ－Ｋｕｔａ算法虽能成功地计算，但不能交换积分顺序。

The interaction energy of two point charged particles is the double integral of z and ρ with poles in the cylindrical coordinate system.It has a simple analytic solution which is difficult to be computed.The commercial programs Mathematica 3.0 and Maple V cannot solve this kind of integrals.The Gauss Legendre algorithm gives a rough result and the Runge Kutta algorithm cannot exchange the integration order though it gives the result successfully.