High-order iterative methods for a nonlinear Kirchhoff wave equation

In this paper we consider the following nonlinear wave equation (1) (…) where μ, f, ũ0, ũ1 are given functions satisfying conditions specified later. In Eq. (1)1, the nonlinear term μ(…) depends on the integral (…) dx. In this paper we associate with equation (1)1 a recurrent sequence {um} defined by (2) (…), 0< x <1, 0< t < T, with um satisfying (1)2,3. The first term u0 is chosen as u0≡0. If f∈CN([0,1]×R+×R), we prove that the sequence {um} converges at a rate of order N to a unique weak solution of problem (1).