Corrector methods with increased ranges of stability

AbstractThe results of a study dealing with the location of stable corrector methods for the numerical solution of ordinary differential equations are reported. From each family of corrector methods of the order q + 1 which require function evaluations at q backpoints (3 ≤ q ⩽ 8), methods are given for which the size of a relative stability disk was numerically optimized. The resulting methods are also shown to have larger regions of absolute stability than do the corresponding Adams-Moulton correctors