Numerical solution of a system of fourth order boundary value problems using cubic non-polynomial spline method

Abstract

A cubic non-polynomial spline technique is developed for the numerical solutions of a system of fourth order boundary value problems associated with obstacle, unilateral and contact problems. The end conditions consistent with the BVP are derived corresponding to the boundary conditions in terms of not only second derivatives but first derivatives as well. The present method has less computational cost and gives better approximations than those produced by other collocation, finite difference and spline methods. The method developed is compared with those developed by Khan et al. [A. Khan, M.A. Noor, T. Aziz, Parametric quintic-spline approach to the solution of a system of fourth-order boundary-value problems, Journal of Optimization Theory and Applications 122(2) (2004) 309–322], Al-Said and Noor [E.A. Al-Said, M.A. Noor, Computational methods for fourth-order obstacle boundary-value problems, Communications in Applied Nonlinear Analysis, 2 (1995) 73–83] and Siddiqi and Ghazala [S.S. Siddiqi, G. Akram, Solution of the system of fourth-order boundary-value problems using non polynomial spline technique, Applied Mathematics and Computation 185 (2007) 128–135] through different examples.