Journal Articles SIAM Journal on Scientific Computing Year : 2024

A first-order reduced model for a highly oscillating differential equation with application in Penning traps

Abstract

We derive a reduced first-order model from a two-scale asymptotic expansion in a small parameter, in order to approximate the solution of a stiff differential equation. The problem of interest is a multi-scale Newton-Lorentz equation modeling the dynamics of a charged particle under the influence of a linear electric field and of a perturbed strong magnetic field. First, we show that in short times, the first-order model provides a much better approximation than the zero-order one, since it contains terms evolving at slow time scales. Then, thanks to the source-free property of the equations, we propose a volume-preserving method using a particular splitting technique to solve numerically the first-order model. Finally, it turns out that the first-order model does not systematically provide a satisfactory approximation in long times. To overcome this issue, we implement a recent strategy based on the Parareal algorithm, in which the first-order approximation is used for the coarse solver. This approach allows to perform efficient and accurate long-time simulations for any small parameter. Numerical results for two realistic Penning traps are provided to support these statements.
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hal-04361370 , version 1 (22-12-2023)

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Sever Hirstoaga. A first-order reduced model for a highly oscillating differential equation with application in Penning traps. SIAM Journal on Scientific Computing, 2024, pp.S225-S245. ⟨10.1137/23M158351X⟩. ⟨hal-04361370⟩
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