The Modified Picard Iteration Method for Solving the Moving Boundary Problems with a Dissolution Term Encountered in the Drug Release Systems

The primary goal of this work is to develop an accurate analytical solution for the moving boundary problems with a dissolution term encountered in drug release from nanoporous structures. To achieve this, we propose applying the modified Picard iteration method for the first time. Using this approach, the moving boundary problem with Dirichlet boundary conditions is transformed into a single integral and then solved iteratively by selecting a suitable starting function. To validate the proposed method, we first analyze the behavior of the equations in specific cases. For these examples, the modified Picard iteration method provides more accurate results than the Picard iteration method, the variational iteration method, and the Adomian decomposition method. Furthermore, the solutions obtained from the proposed method satisfy both boundary conditions, whereas other iterative approaches do not fulfill one of the boundary conditions. The proposed method is also verified by comparing its results with experimental data on drug release from halloysite tubules reported in the literature. The findings indicate that simultaneous dissolution from the moving interface and the perimeter of the pores may be a possible mechanism for drug release from the halloysite tubules.

The Modified Picard Iteration Method for Solving the Moving Boundary Problems with a Dissolution Term Encountered in the Drug Release Systems Keywords:

Modified Picard iteration method , Moving boundary problem , Dirichlet boundary conditions , Approximate solution , Drug release