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The structure of the system of model equations is adaptively changed in the course of integration.

Numerical integration of the model equations is performed by an explicit finite-difference scheme.

However, the numerical solution of model equations is complicated and time consuming.

The formulation of averaged model equations is based on the tolerance averaging approach (Wozniak et al., 2008, 2010).

The verification that computer codes correctly solve their model equations is critical to the continued success of numerical simulation.

The analytical solution to the model equations is shown to give correct predictions in the kinetically controlled case only.

The model equations are solved using an implicit finite difference method and a Newton Raphson algorithm53.

The coupled model equations were solved iteratively.

The model equations are solved using COMSOL Multiphysics.

Initially, the model equations are derived in vector-matrix form to facilitate fast and simple computation.

The model equations were solved numerically.