Numerical methods of high-order accuracy for singular nonlinear boundary value problems

Abstract

is a 2n-th order self-adjoint linear differential operator, and it was shown that the Rayleigh-Ritz-Galerkin method is an efficient scheme, both theoretically and numerically, for solving such problems. Our aim here is to extend the results of [2] and [3] to the case of nonsel[adjoint linear differential operators whose coefficients have a singularity at one or both end points of the interval [0, t ]. For ease of exposition, we shall restrict ourselves here to second order operators, as in the particular case of