On generalized 2-step continuous linear multistep method of hybrid type for the integration of second order ordinary differential equations

摘要

This paper proposes a generalized 2-step continuous multistep method of hybrid type for the direct integration of second-order ordinary differential equations in a multistep collocation technique, which yields block methods. The scheme obtained is used as a single continuous form which serves as a family of formula involving (x, s) such that on substitution of an off-step point s a bi-hybrid continuous scheme is obtained. The discrete equivalent is also obtained thereafter from the continuous family of formula as a block method. It was discovered that Numerical schemes of StÖrmer-Cowell type were recovered via this technique. The scheme obtained is implemented to generate the numerical solution to second order ordinary differential equations. The results obtained are compared with the Renowned Numerov method, known to be of optimal