This paper presents a class of novel, high-order, A-stable defect correction schemes. These schemes are grounded in a newly developed, more versatile class of BDF approaches, which utilize Taylor expansions at time $ t_{n+\beta} $ with $ \beta > 1 $ being an adjustable parameter. The ranges for the stability parameters of these newly proposed defect correction schemes are specified to ensure A-stability. Additionally, numerical experiments are given to illustrate the precision and robustness of the schemes when addressing stiff problems.
Citation: Lin Yao, Xindong Zhang, Xianzhu Li. Stability of implicit defect correction methods based on the new class of BDF methods[J]. Networks and Heterogeneous Media, 2026, 21(3): 755-772. doi: 10.3934/nhm.2026032
This paper presents a class of novel, high-order, A-stable defect correction schemes. These schemes are grounded in a newly developed, more versatile class of BDF approaches, which utilize Taylor expansions at time $ t_{n+\beta} $ with $ \beta > 1 $ being an adjustable parameter. The ranges for the stability parameters of these newly proposed defect correction schemes are specified to ensure A-stability. Additionally, numerical experiments are given to illustrate the precision and robustness of the schemes when addressing stiff problems.
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Lin Yao, Xindong Zhang, Xianzhu Li. Stability of implicit defect correction methods based on the new class of BDF methods[J]. Networks and Heterogeneous Media, 2026, 21(3): 755-772. doi: 10.3934/nhm.2026032
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