A class of fifth order block hybrid Adams Moultonrsquo;s method for solving stiff initial value problems

Abstract

This paper is concern with the derivation of the continuous formulations of hybrid Adams-Moulton Method for step number and incorporating three, two and one off-grid points respectively by multistep collocation method using matrix inversion technique. The discrete schemes used in block form were derived from their respective continuous formulations. The convergence analysis were carried and found that the methods are convergent. The region of absolute stability of the methods were plotted in a block form and they are all - stable. Some linear stiff problems were solved using the schemes. It was observed that the schemes for step number incorporating one off-grid point perform better than the schemes for step number incorporating two and three off-grid points respectively.