Based on the rational system of Legendre rational functions,we construct two set of new interpolation basis functions on the unbounded intervals.Their explicit expressions are derived,and fast and stable algorithms ar...Based on the rational system of Legendre rational functions,we construct two set of new interpolation basis functions on the unbounded intervals.Their explicit expressions are derived,and fast and stable algorithms are provided for computing the new basis functions.As applications,new rational collocation methods based on these new basis functions are proposed for solving various second-order differential equations on the unbounded domains.Numerical experiments illustrate that our new methods are more effective and stable than the existing collocation methods.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12071294)and by the Natural Science Foundation of Shanghai(Grant No.22ZR1443800)The third author is supported in part by the National Natural Science Foundation of China(Grant Nos.11971207,12071172)by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.20KJA110002).
文摘Based on the rational system of Legendre rational functions,we construct two set of new interpolation basis functions on the unbounded intervals.Their explicit expressions are derived,and fast and stable algorithms are provided for computing the new basis functions.As applications,new rational collocation methods based on these new basis functions are proposed for solving various second-order differential equations on the unbounded domains.Numerical experiments illustrate that our new methods are more effective and stable than the existing collocation methods.
