7. 导出具有下列形式的三阶方法：
yn?1?a0yn?a1yn?1?a2yn?2?h(b0yn?b1yn?1?b2yn?2)'''
解： 假设 yn?y(xn)则y(xn?1)?a0y(xn)?a1y(xn?1)?a2y(xn?2)?h[b0y(xn)?b1y(xn?1)?b2y(xn?2)]将y(xn?1)在xn处展开yn?1?(a0?a1?a2)y(xn)?(?a1?2a2?b0?b1?b2)hy(xn)?(a1?4a2?2b1?4b2)h2''''2!y(xn)?(?a1?8a2?3b1?12b3)4''h33!y(x3)'''?(a1?16a2?4b1?32b2)h4!y(4)(xn)?O(h)5?a0?a1?a2?1???a1?2a2?b0?b1?b2?1该公式的三阶方程为 ??a1?4a2?2b1?4b2?1??a?8a?3b?12b?11213?取任一组满足方程组的参数均可。