Abstract
The Dahlquist barrier states that the highest attainable order for an A-stable linear multistep method is limited to 2. In this paper, we adopt the deferred correction approach with the BDF methods to develop A-stable third and fourth-order multistep methods with low stages. The stability of the methods is investigated to show how A-stability can be achieved. Numerical experiments are conducted to validate the accuracy and stability of the proposed methods when applied to stiff problems.
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