Volume 1, Issue 3
Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equation with Steep Gradients

Jia-Chang Sun & Jackson Ken

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J. Comp. Math., 1 (1983), pp. 264-281

Published online: 1983-01

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  • Abstract

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 "Symmetric" implicit one-step schemes having second-order is derived and stability and convergence are studied. As examples, some geometric schemes are given. 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.

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@Article{JCM-1-264, author = {Jia-Chang Sun and Jackson Ken}, 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 = { 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 "Symmetric" implicit one-step schemes having second-order is derived and stability and convergence are studied. As examples, some geometric schemes are given. 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9703.html} }
TY - JOUR T1 - Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equation with Steep Gradients AU - Jia-Chang Sun & Jackson Ken JO - Journal of Computational Mathematics VL - 3 SP - 264 EP - 281 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9703.html KW - AB - 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 "Symmetric" implicit one-step schemes having second-order is derived and stability and convergence are studied. As examples, some geometric schemes are given. 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.
Jia-Chang Sun & Jackson Ken. (1970). Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equation with Steep Gradients. Journal of Computational Mathematics. 1 (3). 264-281. doi:
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