Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems (Q1294523)

This paper deals with schemes based on classes of implicit Runge-Kutta formulae for solving a system of general first-order nonlinear two-point boundary value problems. The authors investigate the problem of deriving interpolating polynomials which are able to provide a continuous solution with a uniform accuracy comparable to that obtained at the mesh points. The quality of the interpolants is presented on seven test problems of second-order singular perturbation type with Dirichlet boundary conditions.