2018/12/22 by В. Л. Макаров, Makarov, Volodymyr, Denys Dragunov +1
Engineering · Mathematics · #65L04 #65L05 #65L10 #65L20 #65L50 #65Y15 #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1812.09498
openalex publication_date 2018/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 https://github.com/imathsoft/MathSoftDevelopment.