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Integration processes of ordinary differential equations based on Laguerre-Radau interpolations


Authors: Ben-Yu Guo, Zhong-Qing Wang, Hong-Jiong Tian and Li-Lian Wang
Journal: Math. Comp. 77 (2008), 181-199
MSC (2000): Primary 65L05, 65D05, 41A30
DOI: https://doi.org/10.1090/S0025-5718-07-02035-2
Published electronically: September 13, 2007
MathSciNet review: 2353948
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Abstract: In this paper, we propose two integration processes for ordinary differential equations based on modified Laguerre-Radau interpolations, which are very efficient for long-time numerical simulations of dynamical systems. The global convergence of proposed algorithms are proved. Numerical results demonstrate the spectral accuracy of these new approaches and coincide well with theoretical analysis.


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Additional Information

Ben-Yu Guo
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People’s Republic of China, Division of Computational Science of E-institute of Shanghai Universities
Email: byguo@shnu.edu.cn

Zhong-Qing Wang
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People’s Republic of China, Division of Computational Science of E-institute of Shanghai Universities
Email: zqwang@shnu.edu.cn

Hong-Jiong Tian
Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People’s Republic of China, Division of Computational Science of E-institute of Shanghai Universities
Email: hjtian@shnu.edu.cn

Li-Lian Wang
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798
Email: lilian@ntu.edu.sg

DOI: https://doi.org/10.1090/S0025-5718-07-02035-2
Keywords: Numerical integrations, ordinary differential equations, modified Laguerre-Radau interpolations
Received by editor(s): August 2, 2005
Received by editor(s) in revised form: December 8, 2006
Published electronically: September 13, 2007
Additional Notes: The work of the first, second, and third authors was partially supported by NSF of China, N.10471095 and N.10771142, SF of Shanghai N.04JC14062, The Fund of Chinese Education Ministry N.20040270002, Shanghai Leading Academic Discipline Project N.T0401 and The Fund for E-institutes of Shanghai Universities N.E03004
The work of the fourth author was partially supported by Start-Up Grant of NTU
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.