Spline solutions of linear tenth-order boundary-value problems^∗

^† To whom all correspondence and requests for off-prints should be addressed.

Abstract

Linear, tenth-order boundary-value problems (special case) are solved, using polynomial splines of degree ten.The spline function values at the midknots of the interpolation interval, and the corresponding values of the even-order derivatives are related through consistency relations. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations.

Four numerical illustrations are given to show the practical usefulness of the algorithm developed. It is observed that this algorithm is second-order convergent.

Keywords:

• Two-point boundary-value problems
• finite-difference methods
• tenth-degree splines

C.R. Categories:

• G.1.7

^∗ Dedicated to the memory of Dr. John A. Gregory.

^† To whom all correspondence and requests for off-prints should be addressed.

^∗ Dedicated to the memory of Dr. John A. Gregory.

^† To whom all correspondence and requests for off-prints should be addressed.

Notes

^∗ Dedicated to the memory of Dr. John A. Gregory.

^† To whom all correspondence and requests for off-prints should be addressed.

Additional information

Notes on contributors

Shahid S. Siddiqi

a,b