Third Derivative Block Hybrid Obrechkoff Methods

This paper presents a family of Third Derivative Block Hybrid Obrechkoff Methods of Adams-type for solving stiff Initial Value Problems (IVPs). Multistep collocation techniques, with power series as basis function, are employed for the derivation of the continuous form of the hybrid methods. The continuous Hybrid Obrechkoff Methods are used to generate several implicit Hybrid Integrators that are expressed in block form and are applied as block integrators at both grid and off-grid points. The Block Methods are of order 2k+3 and their performance on some problems considered shows the accuracy and efficiency of the methods. The basic properties of the developed methods are also discussed.