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Volume 13, Issue 3
High-Accuracy P-Stable Methods with Minimal Phase-Lag for $y "= f(t, y) ^*$

K. L. Xiang

J. Comp. Math., 13 (1995), pp. 232-242.

Published online: 1995-06

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  • Abstract

In this paper, we develop a one-parameter family of P-stable sixth-order and eighth-order two-step methods with minimal phase-lag errors for numerical integration of second order periodic initial value problems: $$ y''=f(t,y), \quad y(t_0)=y_0, \quad y'(t_0)=y'_0. $$ We determine the parameters so that the phase-lag (frequency distortion) of these methods are minimal. The resulting methods are P-stable methods with minimal phase-lag errors. The superiority of our present P-stable methods over the P-stable methods in [1-4] is given by comparative studying of the phase-lag errors and illustrated with numerical examples.

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@Article{JCM-13-232, author = {K. L. Xiang}, title = {High-Accuracy P-Stable Methods with Minimal Phase-Lag for $y "= f(t, y) ^*$}, journal = {Journal of Computational Mathematics}, year = {1995}, volume = {13}, number = {3}, pages = {232--242}, abstract = {

In this paper, we develop a one-parameter family of P-stable sixth-order and eighth-order two-step methods with minimal phase-lag errors for numerical integration of second order periodic initial value problems: $$ y''=f(t,y), \quad y(t_0)=y_0, \quad y'(t_0)=y'_0. $$ We determine the parameters so that the phase-lag (frequency distortion) of these methods are minimal. The resulting methods are P-stable methods with minimal phase-lag errors. The superiority of our present P-stable methods over the P-stable methods in [1-4] is given by comparative studying of the phase-lag errors and illustrated with numerical examples.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9265.html} }
TY - JOUR T1 - High-Accuracy P-Stable Methods with Minimal Phase-Lag for $y "= f(t, y) ^*$ AU - K. L. Xiang JO - Journal of Computational Mathematics VL - 3 SP - 232 EP - 242 PY - 1995 DA - 1995/06 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9265.html KW - AB -

In this paper, we develop a one-parameter family of P-stable sixth-order and eighth-order two-step methods with minimal phase-lag errors for numerical integration of second order periodic initial value problems: $$ y''=f(t,y), \quad y(t_0)=y_0, \quad y'(t_0)=y'_0. $$ We determine the parameters so that the phase-lag (frequency distortion) of these methods are minimal. The resulting methods are P-stable methods with minimal phase-lag errors. The superiority of our present P-stable methods over the P-stable methods in [1-4] is given by comparative studying of the phase-lag errors and illustrated with numerical examples.

K. L. Xiang. (1995). High-Accuracy P-Stable Methods with Minimal Phase-Lag for $y "= f(t, y) ^*$. Journal of Computational Mathematics. 13 (3). 232-242. doi:
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