Conservative numerical methods for nonlinear strings

In this article, a class of numerical schemes for the simulation of nonlinear coupled longitudinal/transverse string vibration is presented. Though there are various ways of arriving at such schemes, special attention is paid here to energy conservation in nonlinear model systems and its transfer to an analogous discrete quantity in a difference scheme. Such exact numerical energy conservation can lead to simple global stability conditions, which can be otherwise difficult to ascertain for nonlinear difference schemes—in particular, such conditions may be arrived at without any reliance on frequency domain concepts i.e., Fourier or Laplace transforms, which are of only moderate utility in the analysis of nonlinear systems. Implementation details are discussed and numerical results are presented.