Cubic splines method for a system of third-order boundary value problems

We use uniform cubic polynomial splines to develop a numerical method for computing approximations to the solution of a system of third-order boundary value problem associated with odd-order obstacle problems. Such problems arise in physical oceanography and can be studied in the framework of variational inequality theory. The convergence analysis of the new method is studied and an upper bound for the error is derived. A numerical example is given to illustrate the efficiency of the new method.

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