利用Legendre小波与Gauss-Legendre求积公式求解三重数值积分  

Numerical Integration Method for Triple Integrals Using Legendre Wavelets and Gauss-Legendre Quadrature

作　　者：许小勇[1] 樊继秋[1] 

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《数学的实践与认识》2017年第13期252-262,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11601076;11561002);江西省自然科学基金(20151BAB211004);江西省教育厅青年科学基金(GJJ4492)

摘　　要：提出利用Legendre小波和Gauss-Legendre求积公式求解几种积分区域的三重数值积分如长方体,四面体,圆柱体,圆锥和椭球体.通过某种线性或非线性变换将空间积分区域变换到空间长方体.利用Gauss-Legendre求积公式将三重积分转换成二重积分,然后利用Legendre小波对二重积分进行逼近.数值算例验证了方法的可行性和有效性.In this paper, a computational method combining Legendre wavelets and Gauss- Legendre quadrature is proposed for numerical integration of arbitrary functions over regions like cuboid, tetrahedron, cylinder, cone and ellipsoid. Integral regions are transformed into the standard integration region by using linear or nonlinear transformation. Gauss-Legendre quadrature is used to convert a triple integral into a double integral which is approximated by Legendre wavelet. Some illustrative examples have been demonstrated to show the ap- plicability and effectiveness of the present method.

关 键 词：三重数值积分 LEGENDRE小波 高斯-勒让德求积公式 变换 雅克比行列式 体积元素 

分 类 号：O172.2[理学—数学]