Abdelmajid El Hajaji, Abdelhafid Serghini, Said Melliani, El Bekkaye Mermri, Khalid Hilal

A Bicubic Splines Method for Solving a Two-Dimensional Obstacle Problem

abstract:
The objective of this paper is to develop a numerical method for solving a bidimensional unilateral obstacle problem. This is based on the bicubic splines collocation method and the generalized Newton method. In this paper, we obtain an approximate expression for solving a bidimensional unilateral obstacle problem. We show that the approximate formula obtained by the bicubic splines collocation method is effective. Next, we prove the convergence of the proposed method. The method is applied to some test examples and the numerical results have been compared with the exact solutions. The obtained results show the computational efficiency of the method. It can be concluded that computational efficiency of the method is effective for the two-dimensional obstacle problem.

Mathematics Subject Classification: 65L10, 34B15, 65M22

Key words and phrases: Obstacle problem, bicubic splines collocation, nonsmooth equation, generalized Newton method