Author : Jiachang Sun
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (227 download)
Book Synopsis Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equations with Steep Gradients by : Jiachang Sun
Download or read book Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equations with Steep Gradients written by Jiachang Sun and published by . This book was released on 1982 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 (GMS) 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. (Author).