Extended convergence of a sixth order scheme for solving equations under ω–continuity conditions

Abstract

The applicability of an efficient sixth convergence order scheme is extended for solving Banach space valued equations. In previous works, the seventh derivative has been used not appearing on the scheme. But we use only the first derivative that appears on the scheme. Moreover, bounds on the error distances and results on the uniqueness of the solution are provided (not given in earlier works) based on ω–continuity conditions. Numerical examples complete this article.

Keywords

• seventh convergence order
• ω–continuity
• local convergence
• banach space
• 65h10
• 65g99
• 49m15