Framework for solving dynamics of Ca2+$$ {\mathrm{Ca}}^{2+} $$ ion concentrations in liver cells numerically: Analysis of a non‐negativity‐preserving non‐standard finite‐difference method

In this article, we consider the numerical approximation of dynamics calcium ion concentrations in liver cells by a non-linear first-order system ordinary differential equations. At first, summarize some analytical results time-continuous problem formulation which are importance to numerically solving system. We continue with presentation our framework contains two ingredients—an optimization approach for determining unique equilibrium state and, as main contribution, non-standard finite-difference scheme time-discretized dynamical prove that proposed conserves non-negativity, and show convergence towards solution. Conclusively, stress theoretical findings examples.