## Quadratic non-polynomial spline approach to the solution of a system of second-order boundary-value problems.(English)Zbl 1100.65067

Summary: A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis of the method is discussed. A numerical example is given to illustrate practical usefulness of the new method.

### MSC:

 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 74M15 Contact in solid mechanics 65L12 Finite difference and finite volume methods for ordinary differential equations
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