Abstract
In this paper, we study a new splitting method for the semi-linear system of ordinary differential equation, where the linear part is stiff. Firstly, the stiff part is split into two parts. The first stiff part, that is called the stiff-cutter and expected to be easily inverted, is implicitly treated. The second stiff part and the remaining nonlinear part are explicitly treated. Therefore, such stiff-cut method can be fast implemented and save the CPU time. Theoretically, we rigorously prove that the proposed method is unconditionally stable and convergent, if the stiff-cutter is chosen to be well-matched in the stiff part. As an application, we apply our method to solve a spatial-fractional reaction-diffusion equation and give a way for how to choose a suitable stiff-cutter. Finally, numerical experiments are carried out to illustrate the accuracy and efficiency of the proposed stiff-cut method.
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Acknowledgements
The authors are grateful to the anonymous referees for their constructive comments which benefit this paper a lot. The second author (corresponding author) Hai-Wei Sun is supported by Science and Technology Development Fund of Macao SAR (Grant No. 0122/2020/A3) and MYRG2020-00224-FST from University of Macau.
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Science and Technology Development Fund of Macao SAR (Grant No. 0122/2020/A3); MYRG2020-00224-FST from University of Macau.
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Sun, T., Sun, HW. A stiff-cut splitting technique for stiff semi-linear systems of differential equations. Numer Algor 95, 1387–1412 (2024). https://doi.org/10.1007/s11075-023-01613-x
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DOI: https://doi.org/10.1007/s11075-023-01613-x