Remark on the convergence of the midpoint method under mild differentiability conditions

[摘要] We establish a convergence theorem for the Midpoint method using a new system of recurrence relations. The purpose of this note is to relax its convergence conditions. We also give an example where our convergence theorem can be applied but other ones cannot. (C) 1998 Elsevier Science B.V. All rights reserved. AMS classification: 65J15; 47B17.

[发布日期] 1998-10-19

[关键词] midpoint method;nonlinear equations in Banach spaces;third-order method;recurrence relations