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

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基金项目: 机械工业部科技基金资助项目(96252011)

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

1.
Zhongkai Agrotechnical College, Guangzhou 510225, P. R. China;
2.
Xiangtan Institute of Machinery and Electricity, Xiangtan 411101, P. R. China;
3.
Department of Mathematics and Physics, Wuyi University, Jiangmen 529042, P. R. China

摘要: 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.
- 指数拟合方法 /
- 阶 /
- A-稳定性
Abstract: 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 presented,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.
- exponentially fitted method /
- order /
- A-stability

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