Parametric continuation of the solitary traveling pulse solution in the reaction-diffusion system using the Newton-Krylov method
Parametric continuation of the solitary traveling pulse solution in the reaction-diffusion system using the Newton-Krylov method
复制标题
使用 Newton-Krylov 方法对反应扩散系统中的孤立行脉冲解进行参数连续
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
N. L. Semendyaeva
中科院分区：
文献类型：
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作者：
A. Makeev;N. L. Semendyaeva
采用GMRES算法（求解线性代数方程组的迭代算法）的无矩阵Newton-Krylov方法，对三组分反应扩散方程组的孤立波行波解进行参数延拓.利用在短时间间隔上的积分结果，我们用另一个具有更方便的（从GMRES算法的谱性质的观点来看）Jacobi矩阵的系统代替了原来的非线性代数方程组系统。所提出的参数延拓被证明是有效的大规模的问题，它使得有可能彻底检查本地化的解决方案对模型的参数的依赖。
The matrix-free Newton-Krylov method that uses the GMRES algorithm (an iterative algorithm for solving systems of linear algebraic equations) is used for the parametric continuation of the solitary traveling pulse solution in a three-component reaction-diffusion system. Using the results of integration on a short time interval, we replace the original system of nonlinear algebraic equations by another system that has more convenient (from the viewpoint of the spectral properties of the GMRES algorithm) Jacobi matrix. The proposed parametric continuation proved to be efficient for large-scale problems, and it made it possible to thoroughly examine the dependence of localized solutions on a parameter of the model.