# On the use of splines for the numerical solution of nonlinear two-point boundary value problems

- Received:
- Revised:

DOI: 10.1007/BF01933195

- Cite this article as:
- Tewarson, R.P. BIT (1980) 20: 223. doi:10.1007/BF01933195

## Abstract

Cubic splines on splines and quintic spline interpolations are used to approximate the derivative terms in a highly accurate scheme for the numerical solution of two-point boundary value problems. The storage requirement is essentially the same as for the usual trapezoidal rule but the local accuracy is improved from*O*(*h*^{3}) to either*O*(*h*^{6}) or*O*(*h*^{7}), where*h* is the net size. The use of splines leads to solutions that reflect the smoothness of the slopes of the differential equations.