Integrable discretization of linear and logistic equations under random intervals with higher-order accuracy

This study proposes an integrable discretization of linear and logistic equations at random intervals with higher-order accuracy. We approximate the exponential function by rational functions using the Padé approximation of any degree and employ them to increase accuracy. We design a new integrable discretization of the linear equations under random intervals with higher-order accuracy. The logistic equation can be discretized through dependent variable transformation while maintaining integrability.