علی شکری

One-step collocation and multistep collocationhave recently emerged as powerful tools for the derivation ofnumerical methods for ordinary differential equations. The sim-plicity and the continuous nature of the collocation process havebeen the main attraction towards this development. In this pa-per we exploited some of these qualities of collocation to derivecontinuous block hybrid collocation methods based on colloca-tion at some polynomial nodes inside the symmetric integrationinterval and the two end points of the interval for dense out-put and for application which favor continuous approximations,like stiff and highly oscillatory initial value problem in ordinarydifferential equations. The analysis of the block hybrid colloca-tion methods show that they are convergent and provide denseoutput at all interior selected points of integration within the in-terval of choice. Preliminary numerical computation carried outis an evidence of better performance of the methods compareto some integrators with strong properties of algebraic stability.Many examples are used to illustrate these properties.