Abstract
Discretization of parabolic free boundary value problems according to [2] gives an implicit procedure which requires the solution of a nonlinear system of inequalities for each time step. The special structure of these inequalities allows us to generalize the theorems about SOR iteration methods, well-known for systems of equations with M-functions (cf.[5]), to the situation of inequalities. First of all we recapitulate the problem and its discretization (cf.[2]) and finally we give the numerical result for a problem of resistance spot welding described in [1] and solved there by an explicit procedure.
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Schäfer, E. (1978). SOR — Verfahren für Nichtlineare Ungleichungssysteme. In: Albrecht, J., Collatz, L., Hämmerlin, G. (eds) Numerische Behandlung von Differentialgleichungen mit besonderer Berücksichtigung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 39. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5566-2_15
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DOI: https://doi.org/10.1007/978-3-0348-5566-2_15
Publisher Name: Birkhäuser, Basel
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