This paper addresses how perturbations in the matrix A propagate along the solution of the n-dimensional linear ordinary differential equation y′(t)=Ay(t),t≥0,y(0)=y0.In other words, for fixed t≥0 and y0∈Rn, we study the conditioning of the problem A↦etAy0.We also study the asymptotic behavior of the conditioning as t→+∞. The analysis is carried out for a normal matrix A.
How perturbations in the matrix of linear systems of ordinary differential equations propagate along solutions
Farooq A.;Maset S.
2022-01-01
Abstract
This paper addresses how perturbations in the matrix A propagate along the solution of the n-dimensional linear ordinary differential equation y′(t)=Ay(t),t≥0,y(0)=y0.In other words, for fixed t≥0 and y0∈Rn, we study the conditioning of the problem A↦etAy0.We also study the asymptotic behavior of the conditioning as t→+∞. The analysis is carried out for a normal matrix A.File in questo prodotto:
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3021333_Farooq-Maset JCAM-Post_print.pdf
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