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A splitting preconditioner for the iterative solution of implicit Runge-Kutta and boundary value methods

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Abstract

We study preconditioned iterative methods for the linear systems arising in the numerical integration of ODEs and time-dependent PDEs by implicit Runge-Kutta and boundary value methods. A preconditioning strategy based on a Kronecker product splitting of the coefficient matrix is proposed, and some useful properties of the preconditioned matrix are established. Numerical examples are presented to illustrate the effectiveness of this approach.

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Acknowledgments

The authors are very grateful to the referees for their constructive comments and valuable suggestions,which greatly improved the original manuscript of the paper. This work was supported by The National Natural Science Foundation (No. 11301575, No. 11171125 and No. 11201162), and the Program of Chongqing Innovation Team Project in University (No. KJTD201308), People’s Republic of China.

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Authors and Affiliations

  1. College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Hao Chen

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  1. Hao Chen
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Correspondence to Hao Chen.

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Communicated by Anne Kværnø.

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Chen, H. A splitting preconditioner for the iterative solution of implicit Runge-Kutta and boundary value methods. Bit Numer Math 54, 607–621 (2014). https://doi.org/10.1007/s10543-014-0467-3

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  • DOI: https://doi.org/10.1007/s10543-014-0467-3

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