重心插值配点法求解二维Sobolev方程  

Barycentric interpolation collocation method for two-dimensional Sobolev equation

作　　者：宋灵宇[1] 武莉莉 卢梦双 SONG Ling-yu;WU Li-li;LU Meng-shuang(College of Science,Chang an University,Xi an 710064,Shaanxi,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《西北师范大学学报（自然科学版）》2021年第6期31-37,44,共8页Journal of Northwest Normal University(Natural Science)

基　　金：陕西省自然科学基金资助项目(2019JQ-755)。

摘　　要：分别采用重心Lagrange插值配点法和重心有理插值配点法求解二维Sobolev方程的数值解.首先,对Sobolev方程在时间方向和空间方向均采用两种插值配点法进行离散,并构造出Sobolev方程的重心插值配点法数值格式;其次,依次选取第二类Chebyshev节点和等距节点进行数值计算,并比较两种插值法在不同节点类型下所得数值解的精度.数值实验结果表明:选取第二类Chebyshev节点时,两种插值法所得数值解的逼近效果都比较好;当选取等距节点时,重心有理插值仍能保持高精度和良好的数值稳定性,而重心Lagrange插值却无法达到.The Lagrange interpolation collocation method and the rational interpolation collocation method are respectively used to solve the numerical solution of the two-dimensional Sobolev equation.First,the Sobolev equation is discretized by two interpolation collocation methods in the time direction and the space direction,and the numerical scheme of the Sobolev equation is constructed.Secondly,select the second type of Chebyshev node and the equidistant node for numerical calculation,and compare the accuracy of the numerical solutions obtained by the two interpolation methods under different node types.Numerical results show that:when selecting the second type of Chebyshev node,the approximation effect of the numerical solution is better;when equidistant nodes are selected,the rational interpolation can still maintain high precision and good numerical stability,but the Lagrange interpolation can not be achieved.

关 键 词：SOBOLEV方程 重心Lagrange插值 重心有理插值 Chebyshev节点 等距节点 

分 类 号：O241.82[理学—计算数学]