JUCS - Journal of Universal Computer Science 16(6): 891-902, doi: 10.3217/jucs-016-06-0891
Newton Method for Nonlinear Dynamic Systems with Adaptive Time Stepping
Wensheng Shen‡, Changjiang Zhang§, Jun Zhang§, Xiaoqian Ma|‡ State University of New York, Brockport, United States of America§ University of Kentucky, Lexington, United States of America| South China University of Technology, Guangzhou, China
Corresponding author: Wensheng Shen ( wshen@brockport.edu ) © Wensheng Shen, Changjiang Zhang, Jun Zhang, Xiaoqian Ma. This article is freely available under the J.UCS Open Content License. Citation:
Shen W, Zhang C, Zhang J, Ma X (2010) Newton Method for Nonlinear Dynamic Systems with Adaptive Time Stepping. JUCS - Journal of Universal Computer Science 16(6): 891-902. https://doi.org/10.3217/jucs-016-06-0891 |  |
Abstract
This paper presents a nonlinear solver based on the Newton-Krylov methods, where the Newton equations are solved by Krylov-subspace type approaches. We focus on the solution of unsteady systems, in which the temporal terms are discretized by the backward Euler method using finite difference. To save computational cost, an adaptive time stepping is used to minimize the number of time steps. The developed program can be applied to solve any nonlinear equations, provided the users could supply the discrete form of the equations. In particular, the nonlinear solver is implemented to solve unsteady reacting flows.
Keywords
Newton-Krylov method, nonlinear dynamics, diffusion flame, iterative solver