In this paper a new five-point approximating subdivision scheme is presented, generating the C 4 curves, which is the extension of the four-point approximating subdivision scheme developed by Siddiqi and Ahmad. The limit function of the new five-point scheme has a support on [−5, 4]. The Laurent polynomial method is used to analyse the smoothness of the new scheme. The Hölder exponent for the scheme is calculated. The usefulness of the scheme is illustrated in the examples.

The non-polynomial spline technique is used for the numerical solution of eighth-order linear special case boundary value problems. The method presented in this paper has also been proven to be secondorder convergent. To compare the method developed in this paper with those developed by Inc and Evans, and Siddiqi and Twizell, two examples are considered and it is observed that our method is more efficient.

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