Journal Article10.1007/S10543-015-0566-9
Numerical methods for nonlinear two-parameter eigenvalue problems
TL;DR: This work considers the computation of critical delays of delay-differential equations with multiple delays and generalizes several numerical methods for nonlinear eigenvalue problems to nonlinear two-parameter eigen value problems.
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Abstract: We introduce nonlinear two-parameter eigenvalue problems and generalize several numerical methods for nonlinear eigenvalue problems to nonlinear two-parameter eigenvalue problems. As a motivation we consider the computation of critical delays of delay-differential equations with multiple delays.
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Citations
Multiparameter Solution Methods for Semistructured Aeroelastic Flutter Problems
Arion Pons,Stefanie Gutschmidt +1 more
TL;DR: This paper presents several new methods for the solution of aeroelastic flutter problems with a partial polynomial structure: problems consisting of a mix ofPolynomial and more complex nonlinear components.
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Nonlinear Multiparameter Eigenvalue Problems in Aeroelasticity
Arion Pons,Stefanie Gutschmidt +1 more
TL;DR: This work devise solution algorithms for nonlinear multiparameter eigenvalue problems arising in the analysis of aeroelastic flutter by devise two iterative algorithms and a restorative algorithm.
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Sensitivity and Backward Perturbation Analysis of Multiparameter Eigenvalue Problems
Arnab Ghosh,Rafikul Alam +1 more
TL;DR: This work presents a general framework for the sensitivity and backward perturbation analysis of linear as well as nonlinear multiparameter eigenvalue problems (MEPs) and proposes a general norm on the space of ME.
4
Nonlinearizing two-parameter eigenvalue problems
Emil Ringh,Elias Jarlebring +1 more
TL;DR: By exploiting the structure of the NEP, the technique to transform a linear two-parameter eigen value problem, into a nonlinear eigenvalue problem (NEP) is investigated, which allows general solution methods for NEPs to be directly applied.
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•Posted Content
Computing several eigenvalues of nonlinear eigenvalue problems by selection
TL;DR: Simple but efficient selection methods based on divided differences for one-parameter nonlinear eigenproblems and how to use divided differences in the framework of homogeneous coordinates may be appropriate for generalized eigenvalue problems with infinite eigenvalues are presented.
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