Abstract
The current paper concerns the uniform and high-order discretization of the novel approach to the computation of Sturm–Liouville problems via Fer streamers, put forth in Ramos and Iserles (Numer. Math. 131(3), 541—565 2015). In particular, the discretization schemes are shown to enjoy large step sizes uniform over the entire eigenvalue range and tight error estimates uniform for every eigenvalue. They are made explicit for global orders 4,7,10. In addition, the present paper provides total error estimates that quantify the interplay between the truncation and the discretization in the approach by Fer streamers.
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Acknowledgments
The author would like to thank the anonymous referees for their comments and suggestions that greatly improved the presentation of the material in this paper, as well as for their thoughts and directions for future work. The author would also like to thank Arieh Iserles and Andreas Asheim for useful discussions. This work was supported by Fundação para a Ciência e a Tecnologia, Portugal through the fellowship SFRH/BD/71692/2010.
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Communicated by: Karsten Urban
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C. P. Ramos, A.G. Uniform and high-order discretization schemes for Sturm–Liouville problems via Fer streamers. Adv Comput Math 44, 395–421 (2018). https://doi.org/10.1007/s10444-017-9547-7
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DOI: https://doi.org/10.1007/s10444-017-9547-7
Keywords
- Numerical method
- Regular Sturm–Liouville problems
- Liouville’s normal form
- Continuous and piecewise analytic potential
- Self-adjoint separated boundary conditions
- Fer expansions
- Fer streamers