Numerical Results via High-Order Iterative Scheme to a Nonlinear Wave Equation with Source Containing Two Unknown Boundary Values

High-order iterative scheme for Kirchhoff-type wave equation with the source containing three unknown values

“…The proofs of these results rely on the fixed point method, the Faedo-Galerkin method, and the arguments related to compactness. This paper can be considered as a relative generalization of the results in [2], [4], [6], [8], [10] and [16].…”

“…Then we have the following theorem. The proof of Theorem 3.1 is based on the Faedo-Galerkin method introduced by Lions [3] and on the similar techniques given in [2], [10] and [16].…”

“…Using the multi-scale invariant theory, the authors proved that the solution of (1.6) for small values of the parameter ε converges to a two-dimensional invariant manifold. It is also necessary to mention the results in [2] and [9], in which the authors investigated the unique solvability of nonlinear wave equations with nonlocal terms u(0, t), u(1, t) and u(η 1 , t), • • • , u(η q , t) respectively, where 0…”