A High Order Iterative Scheme for a Nonlinear Kirchhoff Wave Equation in the Unit Membrane

Abstract

A high-order iterative scheme is established in order to get a convergent sequence at a rate of order $N$ ($N\ge 1$) to a local unique weak solution of a nonlinear Kirchhoff wave equation in the unit membrane. This extends a recent result in (EJDE, 2005, No. 138) where a recurrent sequence converges at a rate of order 2.