Solving an one-dimensional advection-dispersion equation with spline functions

The application of cubic spline polynomials to the numeric solution of a one-dimensional differential dispersion equation is presented. For the non-stationary case, the variation in time was reflected by the spline polynomial coefficients and the discretization in time was obtained using the finite difference method. All the algorithms were implemented with the MATLAB mathematical assistant. The results were compared to tracer test measurements from a real case as well as with the finite element method solution.