W. D. Hoskins

The cubic spline approximation to the fourth-order differential equation yi&ugr; + p(x)y″ + q(x)y′ + r(x)y = t(x) is shown to reduce to the solution of a five-term recurrence relationship. For some special cases the approximation is shown to be simply related to a finite difference representation with a local truncation error of order (1/720)&dgr;8y.