| In this paper we develop a finite-difference scheme to approximate radially symmetric solutions and (1 + 1)-dimensional solutions of the initial-value problem with smooth initial conditions 62w6t2 -12w-b 66t1 2w+g6w 6t+m2w+G' w=0, subjectto: wx&d1;,0 =fx&d1; ,x&d1;∈D, 6w6t x&d1;,0+y x&d1;, x&d1;∈D, in an open sphere D around the origin, where the internal and external damping coefficients beta and gamma, respectively, are constant. The functions &phis; and psi are radially symmetric in D, they are small at infinity, and r&phis;( r) and rpsi(r) are also assumed to be small at infinity. We prove that our scheme is consistent order O (Deltat2) + O (Deltar2) for G ' identically equal to zero, and provide a necessary condition for it to be stable order n. A cornerstone of our investigation will be the study of potential applications of our model to discrete versions involving nonlinear systems of coupled oscillators. More concretely, we make use of the process of nonlinear supratransmission of energy in these chain systems and our numerical techniques in order to transmit binary information. Our simulations show that, under suitable parametric conditions, the transmission of binary signals can be achieved successfully. |
