Stability of implicit defect correction methods based on the new class of BDF methods

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Abstract

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+β with β > 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.

Keywords

A-stable / defect correction schemes / BDF approaches / Taylor expansions / stiff problems

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