Abstract
MHD equilibrium calculations involve elliptic boundary value problems (1) Lu = F(u), Bu = 0 having several solutions. It is explained here why all solutions should be calculated, i.e. including those which are unstable in the sense of Liapunov if they are regarded as equilibrium solutions of (2) \({u_t} = - Lu{\mkern 1mu} + {\mkern 1mu} F(u),{\mkern 1mu} \tilde B(u){\mkern 1mu} = {\mkern 1mu} 0.\) These “unstable” solutions cannot be calculated by certain iterative methods, in principle. The objective here is to find numerical methods allowing efficient computation of the “unstable” solutions. Convergence theorems for such methods will be reported elsewhere by the author. This paper presents solutions and bifurcation diagrams computed by them.
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Meyer-Spasche, R. (1976). Numerical Treatment of Dirichlet Problems with Several Solutions. In: Albrecht, J., Collatz, L. (eds) Numerische Behandlung von Differentialgleichungen Band 2. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 31. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5328-6_9
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DOI: https://doi.org/10.1007/978-3-0348-5328-6_9
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