A high order projection method for nonlinear two point boundary value problems

Summary Approximations to the solutions of a general class of 2m-th order nonlinear boundary value problems are developed in spaces of polynomial splines of degree 2m+1 by requiring the residual to be orthogonal to a class of polynomial splines of degree 2m–1 over the same mesh. Conditions are given for existence and uniqueness of approximations along with theoretical error rates. In some cases these rates are shown to be of the same order as the best approximation to the solution over the approximating spline spaces. Some computational notes and the results of numerical experiments are also given.