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Semi-analytical Time Differencing Methods for Stiff Problems

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Abstract

A semi-analytical method is developed based on conventional integrating factor (IF) and exponential time differencing (ETD) schemes for stiff problems. The latter means that there exists a thin layer with a large variation in their solutions. The occurrence of this stiff layer is due to the multiplication of a very small parameter \(\varepsilon \) with the transient term of the equation. Via singular perturbation analysis, an analytic approximation of the stiff layer, which is called a corrector, is sought for and embedded into the IF and ETD methods. These new schemes are then used to approximate the non-stiff part of the solution. Since the stiff part is resolved analytically by the corrector, the new method outperforms the conventional ones in terms of accuracy. In this paper, we apply our new method for both problems of ordinary differential equations and some partial differential equations.

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Acknowledgments

This work was supported by the National Research Foundation of Korea(NRF) Grant funded by the Korea government(MSIP) (NRF-2012R1A1B3001167).

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Authors and Affiliations

  1. Department of Mathematical Sciences, School of Natural Science, Ulsan National Institute of Science and Technology, UNIST-gil 50, Ulsan, 689-798, Republic of Korea

    Chang-Yeol Jung & Thien Binh Nguyen

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  1. Chang-Yeol Jung
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  2. Thien Binh Nguyen
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Correspondence to Chang-Yeol Jung.

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Jung, CY., Nguyen, T.B. Semi-analytical Time Differencing Methods for Stiff Problems. J Sci Comput 63, 355–373 (2015). https://doi.org/10.1007/s10915-014-9897-y

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  • DOI: https://doi.org/10.1007/s10915-014-9897-y

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