Chebyshev collocation method for the solution of a system of second-order boundary value problems. (English) Zbl 1361.65048
Summary: 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.
MSC:
65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
34B05 | Linear boundary value problems for ordinary differential equations |
65K15 | Numerical methods for variational inequalities and related problems |
74M15 | Contact in solid mechanics |
74S25 | Spectral and related methods applied to problems in solid mechanics |