@Article{JCM-9-185,
author = {},
title = {PA Class of Single Step Methods with a Large Interval of Absolute Stability},
journal = {Journal of Computational Mathematics},
year = {1991},
volume = {9},
number = {2},
pages = {185--193},
abstract = { In this paper, a class of integration formulas is derived from the approximation so that the first derivative can be expressed within an interval [nh,(n+1)h] as $\frac{dy}{dt}=-P(y-y_n)+f_n+Q_n(t)$. The class of formulas is exact if the differential equation has the shown form, where P is a diagonal matrix, whose elements $-pj=\frac{\partial}{\partial y_j}f_j(t_n,y_n),j=1,\cdots,m$ are constant in the interval [nh,(n+1)h], and $Q_n(t)$ is a polynomial in t. Each of the formulas derived in this paper includes only the first derivative f and $-pj=\frac{\partial}{\partial y_j}f_j(t_n,y_n)$. It is identical with a certain Runge-Kutta method. In particular, when $Q_n(t)$ is a polynomial of degree two, one of our formulas is an extension of Treanor's method, and possesses better stability properties. Therefore the formulas derived in this paper can be regarded as a modified or an extended form of the classical Runge-Kutta methods. Preliminary numerical results indicate that our fourth order formula is superior to Treanor's in stability properties. },
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9391.html}
}