论文标题
一种用于计算非线性参数系统分叉的自适应同拷贝方法
An adaptive homotopy method for computing bifurcations of nonlinear parametric systems
论文作者
论文摘要
在本文中，我们提出了一种用于计算非线性系统分叉点的自适应级尺寸同拷贝跟踪方法。这种新方法中有四个组成部分：1）在分叉点附近开发了一种自适应跟踪技术； 2）当自适应跟踪失败时，通货膨胀技术会备份； 3）PUISEUX系列插值用于计算分叉点； 4）分叉点的切线结构在数值上近似以计算不同分支上的溶液。给出了非线性系统的各种数值示例，以说明这种新方法的效率。这种新的自适应同拷贝跟踪方法也应用于非线性PDE系统，并显示出大型非线性离散系统的鲁棒性和效率。
In this paper, we present an adaptive step-size homotopy tracking method for computing bifurcation points of nonlinear systems. There are four components in this new method: 1) an adaptive tracking technique is developed near bifurcation points; 2) an inflation technique is backed up when the adaptive tracking fails; 3) Puiseux series interpolation is used to compute bifurcation points; and 4)the tangent cone structure of the bifurcation point is approximated numerically to compute solutions on different branches. Various numerical examples of nonlinear systems are given to illustrate the efficiency of this new approach. This new adaptive homotopy tracking method is also applied to a system of nonlinear PDEs and shows robustness and efficiency for large-scale nonlinear discretized systems.
