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

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  • Seiler, Werner M.
  • Seiß, Matthias

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.

Suggested Citation

  • Seiler, Werner M. & Seiß, Matthias, 2024. "On the numerical integration of singular initial and boundary value problems for generalised Lane–Emden and Thomas–Fermi equations," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s009630032300615x
    DOI: 10.1016/j.amc.2023.128446
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    References listed on IDEAS

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    1. Amore, Paolo & Boyd, John P. & Fernández, Francisco M., 2014. "Accurate calculation of the solutions to the Thomas–Fermi equations," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 929-943.
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