Abstract
We present backward differentiation formulae (BDF) with nonnegative coefficients for solving initial value problems. These formulae prevent the cancellation of significant figures during the computation. The present formulae are classified into the three types of families: (1) BDF of order 1, (2) Adams type second derivative BDF of order 2, and (3) of order 3. Some of these families are unconditionallyA-stable. We also give the attainable orders with the BDF having nonnegative coefficients.
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Ozawa, K. Backward differentiation formulae with nonnegative coefficients for solving initial value problems. Japan J. Indust. Appl. Math. 9, 397–411 (1992). https://doi.org/10.1007/BF03167274
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DOI: https://doi.org/10.1007/BF03167274