SOME SPECTRAL APPROXIMATIONS FOR DIFFERENTIAL-EQUATIONS IN UNBOUNDED-DOMAINS

This paper deals with three spectral approximations based on expansions by functions defined on the [0, infinity) interval: a tau type method using Laguerre functions, a collocation method using Laguerre polynomials and a collocation method using rational Chebyshev functions. We apply them to several boundary value problems, comparing their applicability, their efficiency and their accuracy. The numerical examples considered include the boundary value problem describing the edge waves on a longshore shear flow and the 'Charney' stability problem of meteorology. We also consider some Laguerre type equations and the computation of the imaginary Bessel function K1