The explicit sixth‐order Numerov‐type family of methods is considered. A new representative from this family is produced and equipped with a cheap step‐size changing algorithm. Actually, after the completion of a step, this remains the same, halved, or doubled. The off‐step points required for such technique are evaluated through local interpolant. Numerical tests over various problems illustrate the efficiency gained by this approach.
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Medvedeva et al. (2019) studied this question.
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