Quintic splines method for second-order boundary value problems

Abstract

We develop a numerical method for computing smooth approximations to the solution of a system of second-order boundary value problems associated with obstacle, unilateral and contact problems based on uniform mesh quintic splines. It is shown that this method gives better approximations than those produced by other collocation, finite-difference and spline methods. A numerical example is given to illustrate the applicability of the new method.

Keywords:

• Quintic spline
• Finite-difference method
• Obstacle problems
• Boundary value problems
• Numerov's method

AMS Subject Classification:

• 65L12
• 49J40

Acknowledgements

The authors are grateful to the referees for their useful suggestions.