The Homotopy Method for the Complete Solution of Quadratic Two-parameter Eigenvalue Problems

Springer Science and Business Media LLC - Tập 90 - Trang 1-25 - 2021
Bo Dong1
1School of Mathematical Sciences, Dalian University of Technology, Dalian, China

Tóm tắt

We propose a homotopy method to solve the quadratic two-parameter eigenvalue problems, which arise frequently in the analysis of the asymptotic stability of the delay differential equation. Our method does not require to form coupled generalized eigenvalue problems with Kronecker product type coefficient matrices and thus can avoid the increasing of the computational cost and memory storage. Numerical results and the applications in the delay differential equations are presented to illustrate the effectiveness and efficiency of our method. It appears that our method tends to be more effective than the existing methods in terms of speed, accuracy and memory storage as the problem size grows.

Tài liệu tham khảo

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