%0 Journal Article %T Recurrence relations for the midpoint method %A J. A. Ezquerro %A M. A. Hernandez %A M. A. Salanova %J Tamkang Journal of Mathematics %D 2000 %I Tamkang University %R 10.5556/j.tkjm.31.2000.33-42 %X In this paper, we present a new convergence analysis and error estimates for the Midpoint method in Banach spaces by using Newton-Kantorovich-type assumptions and a technique based on a new system of recurrence relations. Finally, we give three examples where we improve the error bounds are better given by other authors. %U http://journals.math.tku.edu.tw/index.php/TKJM/article/view/412