Positivity preserving scheme based on exponential integrators

Many phenomena in almost all areas of natural and engineering science are modelled by nonlinear differential equations. However, most of the explicit methods for time integration of nonlinear models fail to preserve some qualitative properties such as positivity of solutions. The major purpose of this study is to suggest a new explicit positivity preserving numerical method based on the exponential integrators. It is shown that the proposed method preserves the positivity of exact solution. Several examples are illustrated to confirm the theoretical result.