Higher order integration methods are not always more accurate or more power efficient. They are typically worse in terms of stability if the step is too big, th

Higher order integration methods are not always more accurate or more power efficient. They are typically worse in terms of stability if the step is too big, they require more computations per step and they may have higher error constant, so they actually often require smaller steps than low order methods. That's why in circuit simulators only methods of order up to 4 are really useful, and most of the time simple schemes of order 2 are used.