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
A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh tra...A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.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.
基金Acknowledgments. The support from the National Natural Science Foundation of China under Grants No.10671146 and No.50678122 is acknowledged. The authors are grateful to the referee and the editor for helpful comments and suggestions.
文摘A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.
