Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method

Version 1 : Received: 3 February 2021 / Approved: 4 February 2021 / Online: 4 February 2021 (15:07:39 CET)

A peer-reviewed article of this Preprint also exists.

Fazio, R. Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method. Math. Comput. Appl. 2021, 26, 18. Fazio, R. Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method. Math. Comput. Appl. 2021, 26, 18.

Journal reference: Math. Comput. Appl. 2021, 26, 18
DOI: 10.3390/mca26010018

Abstract

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.

Subject Areas

Boundary value problems; semi-innite intervals; existence and 22 uniqueness; iterative transformation method; numerical test

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