Parametric continuation of the solitary traveling pulse solution in the reaction-diffusion system using the Newton-Krylov method |
| |
Authors: | A. G. Makeev N. L. Semendyaeva |
| |
Affiliation: | (1) Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia |
| |
Abstract: | 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. |
| |
Keywords: | reaction-diffusion equations localized structures parametric continuation of self-similar solutions Newton-Krylov method GMRES algorithm bifurcation analysis |
本文献已被 SpringerLink 等数据库收录! |