The use of cubic splines in the solution of two-point boundary value problems

A method of obtaining an approximate solution to two-point boundary value problems by use of of cubic splines, which was suggested by Bickley (1968) is developed. Error analysis is carried out and from the results a method of deferred correction is obtained. The use of unequal intervals is considered. An algorithm for computing the solution to prescribed accuracy in the case of equal intervals is described and a numerical example given.