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M. Tsutsumi (1972)
Existence and Nonexistence of Global Solutions for Nonlinear Parabolic EquationsPublications of The Research Institute for Mathematical Sciences, 8
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M. Tsutsumi (1972)
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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 ∞.
Applied Mathematics and Optimization – Springer Journals
Published: Mar 26, 2005
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