Pseudospectral Chebyshev method; Hyperbolic systems; Wave equation; Eigenvalue stability; General linear methods; Order and stage order

The solvability of a certain class of singular nonlinear initial value problems is discussed. Particular attention is paid to the structure of initial conditions necessary for a bounded solution to exist. The implicit Euler rule applied to approximate the solution of the singular system is shown to be stable and to retain its classical convergence order. Moreover, the asymptotic error expansion for the global error of the above approximation is proven to have the classical structure. Finally, experimental results showing the feasibility of the approximation obtained by the Euler method to serve as a basic method for the acceleration technique known as the Iterated Defect Correction are presented.