@Article{JCM-1-3,
author = {Sun, Jia-Chang and Ken, Jackson},
title = {Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equation with Steep Gradients},
journal = {Journal of Computational Mathematics},
year = {1983},
volume = {1},
number = {3},
pages = {264--281},
abstract = {<p style="text-align: justify;">A general theory for nonlinear implicit one-step schemes for solving initial value problems for ordinary differential equations is presented in this paper. The general expansion of &quot;symmetric&quot; implicit one-step schemes having second-order is derived and stability and convergence are studied. As examples, some geometric schemes are given. <br/>Based on previous work of the first author on a generalization of means, a fourth-order nonlinear implicit one-step scheme is presented for solving equations with steep gradients. Also, a hybrid method based on the GMS and a fourth-order linear scheme is discussed. Some numerical results are given. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/1983-JCM-9703},
url = {https://global-sci.com/article/86328/nonlinear-implicit-one-step-schemes-for-solving-initial-value-problems-for-ordinary-differential-equation-with-steep-gradients}
}