Non‐polynomial quintic spline solution for the system of third order boundary‐value problems

In this paper we develop a non‐polynomial quintic spline function to approximate the solution of third order linear and non‐linear boundary value problems associated with odd‐order obstacle problems. Such problems arise in physical oceanography and can be studied in the framework of variational inequality theory. The class of methods are second and fourth order convergent. End equations of the splines are derived and truncation error is obtained. Two numerical examples are given to illustrate the applicability and efficiency of proposed method. It is shown that the new method gives approximations, which are better than those produced by other methods.