A Cubic Spline Method for Solving a Unilateral Obstacle Problem

El Bekkey Mermri, Abdelhafid Serghini, Abdelmajid El hajaji, Khalid Hilal

Department of Mathematics and Computer Science, Faculty of Science, University Mohammed Premier, Oujda, Morocco.
Department of Mathematics, Faculty of Science and Technology, University Sultan Moulay Slimane, Beni-Mellal, Morocco.
Department of Mathematics, Faculty of Science and Technology,University Sultan Moulay Slimane, Beni-Mellal, Morocco.
MATSI Laboratory, ESTO, University Mohammed Premier, Oujda, Morocco.

DOI: 10.4236/ajcm.2012.23028                

Abstract

This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically if a relation-ship between the penalty parameter and the discretization parameter h is satisfied. An error estimate between the penalty solution and the discret penalty solution is provided. To validate the theoretical results, some numerical tests on one dimensional obstacle problem are presented.

Keywords

Obstacle Problem; Spline Collocation; Nonsmooth Equation; Generalized Newton Method

Conflicts of Interest

The authors declare no conflicts of interest.

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