@Article{JCM-3-4,
author = {},
title = {A-Stable and L-Stable Block Implicit One-Step Method},
journal = {Journal of Computational Mathematics},
year = {1985},
volume = {3},
number = {4},
pages = {328--341},
abstract = {<p style="text-align: justify;">A class of methods for solving the initial problem for ordinary differential equations are studied. We develop k-block implicit one step methods whose nodes in a block are nonequidistant. When the components of the node vector are related to the zeros of Jacobi&#39;s orthogonal polynomials, we can derive a subclass of formulas which are A or L-stable. The order can be arbitrarily high with A- or L-stability. We suggest a modified algorithm which avoids the inversion of a $km×km$ matrix during Newton-Raphson iterations, where $m$ is the number of differential equations. When k=4, for example, only a couple of $m×m$ matrices have to be inversed, but four values can be obtained at one time.</p>},
issn = {1991-7139},
doi = {https://doi.org/1985-JCM-9629},
url = {https://global-sci.com/article/86254/a-stable-and-l-stable-block-implicit-one-step-method}
}