Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations

Abstract

This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection−diffusion−reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers’ and Maxwell−Stefan diffusion equations.

Keywords

• time adaptive integration
• adaptive iterative splitting
• operator-splitting method
• error control
• convection–diffusion–reaction equations
• iterative solver method
• nonlinear equations