On the Numerical Integration of Singular Initial and Boundary Value
Problems for Generalised Lane-Emden and Thomas-Fermi Equations
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Co-author(s): Matthias Seiß |
Reference: Applied Mathematics and Computation, 466 (2024) 128446 (16 pages) |
Description: We propose a geometric approach for the numerical integration of singular initial
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. |
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