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Efficient computation of delay differential equations with highly oscillatory terms

Marissa Condon, Alfredo Deaño, Arieh Iserles, Karolina Kropielnicka (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory forcing terms. The computation of such problems using standard numerical methods is exceedingly slow and inefficient, indeed standard software is practically useless for this purpose. We propose an alternative, consisting of an asymptotic expansion of the solution, where each term can be derived either by recursion or by solving a non-oscillatory...

Efficient computation of delay differential equations with highly oscillatory terms

Marissa Condon, Alfredo Deaño, Arieh Iserles, Karolina Kropielnicka (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory forcing terms. The computation of such problems using standard numerical methods is exceedingly slow and inefficient, indeed standard software is practically useless for this purpose. We propose an alternative, consisting of an asymptotic expansion of the solution, where each term can be derived either by recursion or by solving a non-oscillatory...

Efficient computation of delay differential equations with highly oscillatory terms

Marissa Condon, Alfredo Deaño, Arieh Iserles, Karolina Kropielnicka (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory forcing terms. The computation of such problems using standard numerical methods is exceedingly slow and inefficient, indeed standard software is practically useless for this purpose. We propose an alternative, consisting of an asymptotic expansion of the solution, where each term can be derived either by recursion or by solving a non-oscillatory...

Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis

James Adduci, Boris Mityagin (2012)

Open Mathematics

For any complex valued L p-function b(x), 2 ≤ p < ∞, or L ∞-function with the norm ‖b↾L ∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d 2/dx 2 + x 2 + b(x) in L 2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L 2(ℝ).

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