A technique for the numerical solution of initial-value problems based on a class of Birkhoff-type interpolation method
The authors analyse various properties (construction, uniqueness, error) of a Birkhoff interpolation scheme such that a polynomial and its first \(m-1\) derivatives match a given function and corresponding derivatives at a given point, as well as the \(n\)th derivatives matching at a set of distinct nodes. This interpolation scheme is used to construct numerical methods for the general \(n\)th order initial value problem and a number of test problems (only one of which is a system) are solved.
scientific article; zbMATH DE number 6138052