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SUMMARYA technique is described for solving the compressible flow equations in subsonic flow. The general quasi-linear equation V . g V v = 0 is considered with g a function of V v . V v , and iterations of the form V . g , V U , +~ = 0 are analysed, where go is suitably chosen and g , defined from u, for n > 1. This approach is applied to the compressible flow equations in terms of a velocity potential 4 : monotonic convergence is predicted and at each iteration the error is multiplied by a factor less than the square of the greatest Mach number in the solution.by a finite difference method. The alternative of working in terms of the stream function $ is discussed, and also discretization by the finite element method.

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A finite-difference method, using the transverse field components as variables, is developed for calculating the properties of waveguides containing nonuniform dielectrics. It is shown how an essential consistency condition in the discretisation may be satisfied. Results are given for the dispersion of the quasi-TEM waves and the cutoff frequencies of higher waves in some typical problems. Other methods of calculation are discussed, and, in particular, it is shown that the use of the axial field components as variables complicates the problem. List of symbolsh = thickness of dielectric layer w -width of strip t = thickness of strip e, e 0 = permittivites [x = permeability C, C o = capacitances per unit length x, y = Cartesian co-ordinates in the waveguide crosssection s, n = Cartesian co-ordinates rotated from the (fixed) set x, y z = axial co-ordinate E x etc. = component of electric field H x etc. = component of magnetic field co = angular frequency y = 27r/wavelength / = y-i t = time = static potential v = vector of field components v t k -number of strips p = number of nodes used on mesh b -number of points lying on conducting boundaries m = number of mesh areas c 0 = velocity of light x h y t = components of E x , E y (used in Fig. 2a in preference tO Vj)

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