High Order Numerical Differentiation Type Formulas with an Off-step Point for Stiff Ordinary Differential Equations

1 June 1976

journal article
Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics

Vol. 17 (3) , 281-293
https://doi.org/10.1093/imamat/17.3.281

Abstract

Linear k-step implicit numerical differentiation (N.D.) formulas which are of order k are stable for k ≤ 6 (Henrici, 1962). In this paper N.D. type formulas are derived by introducing the value of the derivative at an off-step point. It is found that the resulting k-step implicit formulas have order k+2 and are stable for k ≤ 16. Stiff stability is achieved for k ≤ 7, by introducing a suitable corrector at the off-step point. The necessary predictors are also derived.

Keywords

NUMERICAL DIFFERENTIATION
HIGH ORDER
ORDER NUMERICAL
DIFFERENTIAL EQUATIONS
STEP POINT
TYPE FORMULAS
STIFF ORDINARY
DIFFERENTIATION TYPE

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