A class of methods based on a septic non-polynomial spline function for the solution of sixth-order two-point boundary value problems

Abstract

Two new second- and fourth-order methods based on a septic non-polynomial spline function for the numerical solution of sixth-order two-point boundary value problems are presented. The spline function is used to derive some consistency relations for computing approximations to the solution of this problem. The proposed approach gives better approximations than existing polynomial spline and finite difference methods up to order four and has a lower computational cost. Convergence analysis of these two methods is discussed. Three numerical examples are included to illustrate the practical use of our methods as well as their accuracy compared with existing spline function methods.

Keywords:

• Septic non-polynomial spline
• Finite difference
• Two-point boundary value problem
• Sixth order

AMS Subject Classification :

• 65L10

Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions which improved and enhanced this work.

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