Iterative operator-splitting methods for nonlinear differential equations and applications of deposition processes

Abstract

In this article we consider iterative operator-splitting methods for nonlinear differential equations. The main feature of the proposed idea is the embedding of Newton's method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator-splitting methods by providing improved results and convergence rates. We apply our results to deposition processes.