, Volume 20, Issue 2, pp 223-232

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

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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 fromO(h 3) to eitherO(h 6) orO(h 7), whereh is the net size. The use of splines leads to solutions that reflect the smoothness of the slopes of the differential equations.