PROPAGATION AND STABILITY OF WAVELIKE SOLUTIONS OF FINITE-DIFFERENCE EQUATIONS WITH VARIABLE-COEFFICIENTS

An asymptotic approach is used to analyze the propagation and dissipation of wavelike solutions to finite difference equations. It is shown that to first order the amplitude of a wave is convected at the local group velocity and varies in magnitude if the coefficients of the finite difference equation vary. Asymptotic boundary conditions coupling the amplitudes of different wave solutions are also derived. Equations are derived for the motion of wavepackets and their interaction at boundaries. Comparison with numerical experiments demonstrates the success and limitations of the asymptotic approach. Finally, a global stability analysis is developed. © 1985