In the present paper we generalize the classical leapfrog method for u, = ux. For every r3=0 and 5 3=0 with r + s^l, we obtain an r + j-order explicit two-step method that uses r points to the left and s points to the right. The stability of such methods is analysed by using the order-star theory. It follows that the methods are stable and conservative if and only ifr^s^r + L We also present results on the group velocity of these methods. 1.
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Arieh Iserles (1986) studied this question.