Abstract
The theory of generalized multistep methods using an off-grid point is extended to the special second-order equation y″ = f ( x , y ). New high-order methods for solving this equation, based on quasi-Hermite interpolating polynomials, are shown to exist, as well as new explicit generalized methods for a first-order equation. Some results in the theory of quasi-Hermite interpolation are given, and results of computations of an unperturbed orbit trajectory are presented.

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