Errors in Calculations of Predeposition Diffusion Profiles by Iterative Numerical Methods

The errors in numerical calculations of one-dimensional predeposition profiles have been determined for the direct method of finite differences and for the finite element method. These errors can be calculated because the exact solution of this linear diffusion problem is known to be the complementary error function. The relative errors at the nodes of the depth-time lattice are illustrated. The results are useful for assessing the errors of calculations of multidimensional profiles by these iterative methods, where no exact solutions are known. The results indicate that accurate calculations of such profiles will require such fine lattices and large numbers of time steps that the usefulness of the iterative methods becomes doubtful.