Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators

This research looked at nonlinear ordinary differential equations with global differential operators and the Dirac-delta and exponential decay kernels. A recently developed numerical approach based on the repetitive use of the well-known midpoint quadrature approximation. Although no theoretical analysis was offered, the method was applied to solve several nonlinear equations in chaos and epidemiology. The observed findings demonstrate the effect of the chosen function $g\left(t\right)$, for example, a simple SIR model produced chaotic and crossover behaviors.