A four-step trigonometric fitted P-stable Obrechkoff method for periodic initial-value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:187

Article

Dai, YM ; Wang, ZC ; Wu, DM

关键词: Obrechkoff method;    P-stable;    high-order derivative;    first-order derivative formula;    second-order initial value problem with periodic solutions;   

DOI  :  10.1016/j.cam.2005.03.043

来源: Elsevier

【 摘 要 】

In this paper, we present a new P-stable Obrechkoff four-step method, which greatly improves the performance of our previous Obrechkoff four-step method and extends its application range. By trigonometric fitting, we extend the interval of periodicity of the previous four-step method from about H-2 similar to 16 to infinity and at the same time, we keep all its advantage in the accuracy and efficiency. We have tested the new method by four well-known problems, (1) the test-equation; (2) Stiefel and Bettis problem; (3) Duffing equation without damping; and (4) Bessel equation. The numerical results show that the new method is more accurate than any previous method. It also has great advantage in stability and efficiency. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free