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Mathematics > Numerical Analysis

arXiv:1812.09498 (math)
[Submitted on 22 Dec 2018 (v1), last revised 21 Aug 2020 (this version, v6)]

Title:SI-method for solving stiff nonlinear boundary value problems

Authors:Volodymyr Makarov, Denys Dragunov
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Abstract:The paper contains a thorough theoretical analysis of the SI-method, which was firstly introduced in arXiv:1601.04272v8 and proved to be remarkably stable and efficient when applied to some instances of stiff boundary value problems (like the Troesch's problem). By suggesting a more general view on the SI-method's idea and framework, we managed to obtain sufficient conditions for the method to be applicable to a certain class of two-point boundary value problems. The corresponding error estimates are provided. Special attention is devoted to the exploration of the method's capabilities via a set of numerical examples. The implementation details of the method are discussed in fair depth. An open-source C++ implementation of the SI-method is freely available at the public repository this https URL.
Comments: 33 pages, 10 figures, 4 tables, draft
Subjects: Numerical Analysis (math.NA)
MSC classes: 65L04, 65L05, 65L10, 65L20, 65L50, 65Y15
Cite as: arXiv:1812.09498 [math.NA]
  (or arXiv:1812.09498v6 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.09498

Submission history

From: Denys Dragunov V. [view email]
[v1] Sat, 22 Dec 2018 10:57:27 UTC (8 KB)
[v2] Mon, 6 May 2019 18:21:38 UTC (15 KB)
[v3] Tue, 6 Aug 2019 19:20:50 UTC (28 KB)
[v4] Sun, 22 Mar 2020 14:31:55 UTC (76 KB)
[v5] Sun, 3 May 2020 10:43:27 UTC (81 KB)
[v6] Fri, 21 Aug 2020 07:05:36 UTC (81 KB)
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