Abstract
We focus on the solution of multiparameter spectral problems, and in particular on some strategies to compute coarse approximations of selected eigenparameters depending on the number of oscillations of the associated eigenfunctions. Since the computation of the eigenparameters is crucial in codes for multiparameter problems based on finite differences, we herein present two strategies. The first one is an iterative algorithm computing solutions as limit of a set of decoupled problems (much easier to solve). The second one solves problems depending on a parameter \(\sigma \in [0,1]\), that give back the original problem only when \(\sigma =1\). We compare the strategies by using well known test problems with two and three parameters.
This research was supported by the project “Equazioni di Evoluzione: analisi qualitativa e metodi numerici” of the Università degli Studi di Bari.
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Notes
- 1.
In case of singular problem, the solution is not continuous at some endpoints but the strategies discussed below continue to work well.
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Amodio, P., Settanni, G. (2020). Numerical Strategies for Solving Multiparameter Spectral Problems. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_23
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