Spline Function Methods for Nonlinear Boundary-Value Problems The solution of the nonlinear differential equation Y"=F(x,Y,Y') with two-point boundary conditions is approximated by a quintic or cubic spline function y(x). The method is well suited to nonuniform mesh size and dynamic mesh size allocation. For uniform mesh size h, the error in the quintic spline y(x) is O(h^4), with typical error one-third that from Numerov's method. Requiring the differential equation to be satisfied at the mesh points results in a set of difference equations, which are block tridiagonal and so are easily solved by relaxation or other standard methods. CACM June, 1969 Blue, J. L. boundary value problems, differential equations, finite differences, functional approximation, iterative methods, nonlinear equations, spline functions 5.13 5.15 5.17 CA690605 JB February 17, 1978 11:07 AM 1888 5 1888 1888 5 1888 1888 5 1888