On the numerical integration of singular initial and boundary value problems for generalised Lane–Emden and Thomas–Fermi equations

Werner M. Seiler and Matthias Seiß

Applied Mathematics and Computation, 2024, vol. 466, issue C

Abstract: We propose a geometric approach for the numerical integration of singular initial and boundary value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at a stationary point of an associated vector field and thus into one which can be solved in an efficient and robust manner. Using the shooting method, our approach also works well for boundary value problems. As examples, we treat some (generalised) Lane–Emden equations and the Thomas–Fermi equation.

Keywords: Singular initial value problems; Singular boundary value problems; Vessiot distribution; Unstable manifold; Numerical integration; Lane–Emden equation; Thomas–Fermi equation; Majorana transformation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:466:y:2024:i:c:s009630032300615x

DOI: 10.1016/j.amc.2023.128446

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