A capacitance matrix method is used to eliminate the problem of boundary conditions. This leads to solving a series of Helmholtz problems. The spatial discretisation makes use of the wavelet method in the periodic direction and the spectral collocation Chebychev method in the non periodic direction. The resolution of the discrete Helmholtz problem is done by means of the diagonalisation technique in the non periodic direction. The system then splits into a sequence of one dimensional periodic Helmholtz problems which are efficiently inverted using FFTs.
Numerical tests show both the stability and the accuracy of the method.
We show that a viscoelastic model gives a good account of both the longitudinal-current autocorrelation function and the dynamic structure factor in the region of the crossover. Evidence is also given for a weakly dispersing excitation observed in these experiments being a liquid state remnant of an oxygen-related optic mode in ice. The kinetics of dusty plasma in low pressure RF discharges is studied by solving self-consistantly the time dependent electron Boltzmann and dust charging equations. The temporal behaviours of the electron energy distribution and the dust surface potential are investigated. The electron temperature and the dust particle charge are both shown to be modulated and out of phase with each other.