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