Multi-point Taylor approximations in one-dimensional linear boundary value problems

We consider second order linear differential equations in a real interval I with mixed Dirichlet and Neumann boundary data. We consider a representation of its solution by a multi-point Taylor expansion. The number and location of the base points of that expansion are conveniently chosen to guarantee that the expansion is uniformly convergent ∀ x ∈ I. We propose several algorithms to approximate the multipoint Taylor polynomials of the solution based on the power series method for initial value problems. 2000 AMS Mathematics Subject Classification: 34A25, 34B05, 41A58.