Possibilities and limits of the transfer coefficients method

Abstract

In order to describe the basic numerical phenomena (instabilities, divergence, distortions) intervening in the finite-differences (FD) simulations of the pulse propagation through different media, we introduced the method of transfer coefficients, relating the simulated pulse components to those of the true pulses. The accomplished study pointed out: a) the remarkable possibilities of this method to describe accurately (sometimes, even exactly) the stability and convergence of some schemes, for linear homogeneous media and equal physical and FD speeds, b) the existing, but limited (due to some computation difficulties) possibilities to describe also the distortions intervening for values C < 1 of the Courant number), c) the practical impossibility to use this method for nonlinear media. Some newly obtained results concerning certain power laws and auto-catalytic growth processes pointing out the Complexity of the studied algorithms were also reported.