重心插值配点法求解二维非线性椭圆型方程  

Barycentric Interpolation Collocation Method for Solving Two Dimensional Nonlinear Elliptic Equation

作　　者：宋灵宇[1] 王彩珍 李彬彬 SONG Ling-yu;WANG Cai-zhen;LI Bin-bin(College of Science,Changan University,Xian 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2019年第3期189-195,共7页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：陕西省自然科学基金资助项目(2016JM6081)

摘　　要：首先利用重心插值配点法离散二维非线性椭圆型方程和边界条件,其次采用完全线性化迭代和Newton-Raphson迭代求出方程的近似解.实验结果表明:重心插值配点法理论简单,计算精度高; Newton-Raphson迭代法无论是在计算效率上,还是在计算精度上,都优于完全线性化迭代.Firstly,barycentric interpolation collocation method was used to discretize a two dimensional nonlinear elliptic equation and its boundary conditions.Secondly,the approximate solution of the equation was obtained by using the complete linearization iteration and the Newton-Raphson iteration.The research results showed that the barycentric interpolation collocation method was simple in theory and highly accurate in calculation.The Newton-Raphson iterative method was better than the complete linearization iteration either in the calculation efficiency or in the calculation accuracy.

关 键 词：重心插值配点法 线性化迭代 Newton-Raphson迭代 

分 类 号：O241.82[理学—计算数学]