2020/11/13 by Riccardo Fazio, Fazio, Riccardo
Computer Science · Engineering · Mathematics · #34B15 #65L08 #65L10 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations #cs.NA #math.NA #msc:34B15 #msc:65L08 #msc:65L10
paper · pdf · doi:10.48550/arxiv.2011.07725
28 pages, 7 figures and 4 tables. arXiv admin note: substantial text overlap with arXiv:2003.07971, arXiv:1212.5057
arxiv created 2020/11/13 · openalex publication_date 2020/11/13 · arxiv updated 2020/11/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context the numerical test is illustrated by two examples where we find meaningful numerical results.