Adam’s block with first and second derivative future points for initial value problems in ordinary differential equations

Abstract

In this paper, we develop Adam’s Block with first and second derivative future points for solving linear and non-linear first order initial value problems in ordinary differential equations. The derivation of the method is based on Taylor series approach. The region of absolute stability of the method is investigated using the boundary locus method and this family of methods have been found to be A-stable for r=2,3,4 and 5. Numerical experiments are demonstrated with the method and computational comparisons are presented with some existing numerical methods. The computational comparison depicts the efficiency of the methods on initial value problems in ordinary differential equations (ODEs).