Mathematics of Computation

Author(s): M. Z. Liu; Z. W. Yang; Y. Xu.
Journal: Math. Comp. 75 (2006), 1201-1215.
MSC (2000): Primary 65L02, 65L05; Secondary 65L20
Posted: May 3, 2006
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Abstract: In the present paper, the modified Runge-Kutta method is constructed, and it is proved that the modified Runge-Kutta method preserves the order of accuracy of the original one. The necessary and sufficient conditions under which the modified Runge-Kutta methods with the variable mesh are asymptotically stable are given. As a result, the $\theta$ -methods with $\tfrac12\leq\theta\leq 1$ , the odd stage Gauss-Legendre methods and the even stage Lobatto IIIA and IIIB methods are asymptotically stable. Some experiments are given.

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Retrieve articles in Mathematics of Computation with MSC (2000): 65L02, 65L05, 65L20

M. Z. Liu
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
Email: mzliu@hope.hit.edu.cn

Z. W. Yang
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China

Y. Xu
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China

DOI: 10.1090/S0025-5718-06-01844-8
PII: S 0025-5718(06)01844-8
Keywords: Pantograph equation, asymptotical stability, Runge-Kutta methods.
Received by editor(s): September 13, 2004
Posted: May 3, 2006
Additional Notes: This paper was supported by the National Natural Science Foundation of China (10271036).
Copyright of article: Copyright 2006, American Mathematical Society

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