High order compact finite difference schemes for a system of third order boundary value problem

High order compact finite difference schemes are devised for general third order differential equations raised in the study of obstacle boundary value problems. These high order compact schemes are constructed by a modification, without additional workload in computation, of the second-order scheme developed in Noor and Al-Said (2002) [10]. The convergence rates of these schemes are shown to be third- and fourth-order, respectively. Numerical experiments show that the proposed schemes are of high accuracy and are efficient.