Chebyshev collocation method for the solution of a system of second-order boundary value problems

Abstract

In this paper, we present a new numerical approach based on Chebyshev polynomials of the first kind for solving a system of second-order boundary value problems associated with obstacle, unilateral and contact problems. The applicability of the method is demonstrated on two numerical examples. The results obtained show the effectiveness, reliability and superiority of the new method over other existing methods in the literature. In addition, the method is simple and easy to implement.