New predictor corrector formulas for initial value problems in ordinary differential equations

Henrici [5] discussed the formulation of Adams-Bashforth-Moulton and Nystrom-Milne predictor corrector formulas. Gear [2, 3, 4] incorporated the variable order Adams-Moulton corrector for non-stiff initial value problems in his well known and well tested package—DIFSUB. Some New Predictor Corrector Formulas are hereby proposed for an arbitrary—step-number k > 3. A matrix representation in the spirit of Gear [2, 3, 4] is incorporated so as to facilitate variable step, variable order modes. For even step-numbers, the proposed algorithms are nearly symmetric and hence perform better than the Adams-Bashforth-Moulton predictor corrector formulas on oscillatory initial value problems. AMS (MOS) Subject Classification (1970) Primary 65L05; Secondary 65D30