  In this paper we develop an $hp$-adaptive procedure for the numerical
solution of general, semilinear elliptic boundary value problems in 1d, with
possible singular perturbations. Our approach combines both a prediction-type
adaptive Newton method and an $hp$-version adaptive finite element
discretization (based on a robust a posteriori residual analysis), thereby
leading to a fully $hp$-adaptive Newton-Galerkin scheme. Numerical experiments
underline the robustness and reliability of the proposed approach for various
examples.
