Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equation with Steep Gradients
Year: 1983
Author: Jia-Chang Sun, Ken Jackson
Journal of Computational Mathematics, Vol. 1 (1983), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1983-JCM-9703
Journal of Computational Mathematics, Vol. 1 (1983), Iss. 3 : pp. 264–281
Published online: 1983-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18