Analysis of a Finite‐Difference Method Based on Nonlocal Approximations for a Nonlinear, Extended Three‐Compartmental Model of Ethanol Metabolism in the Human Body

ABSTRACT In this work, we combine two different existing two‐compartmental models of ethanol metabolism and propose a nonlinear three‐compartmental model of ethanol metabolism in the human body based on Michaelis‐Menten kinetics for elimination of ethanol in liver cells. Hence, we obtain a system of nonlinear differential equations, which describes the approximate dynamics of ethanol elimination in the human body. Furthermore, we show that our time‐continuous model possesses a unique nonnegative solution globally in time and has exactly one stable fixed point whose stability is shown. Afterward, we suggest a nonstandard finite‐difference method based on Mickens' methodology for its numerical solution and examine all properties of our time‐continuous model, which are preserved in the time‐discrete case. Additionally, we show that the proposed scheme converges linearly towards the solution of the time‐continuous model. Conclusively, we underline our theoretical findings by numerical examples.