A linear recursive scheme associated with the love equation

On a high-order iterative scheme for a nonlinear love equation

“…This condition can be relaxed if we only consider the existence of a solution, see [10]- [13], [14], [17], [18].…”

“…The SRLWE also arises in many other areas of mathematical physics [4], [9], [14]. Note that (1.8) is a special form of the equation discussed in [10].…”

“…By using the Fourier method, Radochová [17] Equations of Love waves or Love-type waves have been studied by many authors, we refer to [3], [6], [11], [10], [16], and references therein.…”

“…In [10], by combining the linearization method for the nonlinear term, the FaedoGalerkin method and the weak compactness method, the existence of a unique weak solution of a Dirichlet problem for the nonlinear Love equation u tt − u xx − u xxtt = f (x, t, u, u x , u t , u xt ) is proved. We note, however, the recurrent sequence obtained here converges only at a rate of order 1.…”

“…Motivated by results for Love equations in [11], [10], and based on the use of a high-order iterative scheme in [13], [12], [19], [20], in this note, we will establish a similar scheme to get the convergence of order N for problem (1.1)-(1.3). To achieve this purpose, we define a recurrent sequence {u m } associated with equation (1.1) as follows: …”