Abstract
This paper studies a finite difference approximation to the similinear heat equation (1) with special emphasis on the case when the exact solution blows up with the blowing-up timeT ∞. The key results will be given in Propositions 1 and 2. Proposition 1 states the local convergence, i.e., the convergence of the proposed finite difference solution to the exact solution in any fixed time interval 0 ⩽t ⩽ T, whereT < T ∞. Proposition 2 states the convergence of the numerical blowing-up time to the exact oneT ∞.
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Communicated by M. Yamaguti
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Nakagawa, T. Blowing up of a finite difference solution tou t = uxx + u2 . Appl Math Optim 2, 337–350 (1975). https://doi.org/10.1007/BF01448176
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DOI: https://doi.org/10.1007/BF01448176