Ball convergence for a third order method based on Newton's method and the Adomian decomposition method

摘要

The aim of this paper is to extend the usage of a third order method based on the Adomian decomposition in cases not covered before. The hypotheses are based only on the first derivative while in earlier works hypotheses requiring the existence of the fifth derivative are utilised to show the convergence of the method. Moreover, we also provide radii of convergence as well as error estimates based on Lipschitz constants not given before in earlier works. Numerical examples emphasising the superiority of the new results over the earlier ones complete this paper.