Numerical solutions of third-order system of boundary value problems

We develop a two stage numerical method for computing approximate solutions of a system of third-order boundary value problems associated with odd order obstacle problems. Such a problem arise in physical oceanography and can be studied in the framework of variational inequality theory. We show that the present method is of order two and gives numerical results which are better than the other available results. Numerical example is presented to illustrate the applicability of the new method. Our results can be viewed as an important and significant refinement of the previously known results.