“…The second‐order differential equation, , is converted to a third‐order, fourth‐order, or fifth‐order (or even higher order) equivalent differential equation while holding the Jacobians ( J 11 , J 12 ) fixed over the interval of integration to match the Jacobian of the original equation, and maintaining the final value of the original differential equation. These formulations, together with corresponding higher order derivatives, are summarized as follows: …”