怎样利用函数exp(q)的含参有理逼近构造高阶指数拟合方法

On Construction of High Order Exponentially Fitted Methods Based on Parameterized Rational Approximations to exp(q)

得到了指数函数ｅｘｐ（ ｑ） 的含双参数α、β的（４ ，４） 有理逼近的表达式及其为 Ａ＿ 可接受的充要条件，由此构造了精确阶可达６ 至８ 阶的四阶导数单步指数拟合方法与三阶导数混合单步指数拟合方法· 研究了这两种算法的拟合阶及其为 Ａ＿ 稳定的充要条件· 最后讨论了四阶导数方法的中间性与误差界·

By the discussion of the formula and properties of (4,4) parametric form rational approximation to function exp(q), the fourth order derivative one_step exponentially fitted method and the third order derivative hybrid one_step exponentially fitted method are constructed, their order p satisfying 6≤p≤8. The necessary and sufficient conditions for the two methods to be A_stable are given. Finally, for the fourth order derivative method, the error bound and the necessary and sufficient conditions for it to be median are discussed.