Efficient Numerical Methods for Evolution Partial Differential Equations
Author | : Lhannes Karakashian |
Publisher | : |
Total Pages | : 5 |
Release | : 1989 |
Genre | : |
ISBN | : |
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The convergence estimates obtained for the Korteweg-de Virus equation have been generalized, under the assumption that the solution u is sufficiently regular. For p 4, it is not known whether a global smooth solution exists corresponding to smooth initial data. It is in fact conjectured that for these cases, the solution may develop a singularity in finite time. A code that uses a spatially and temporally adaptive strategy has been implemented. We are currently investigating the stability of solitary type solutions. As conjectured, these solutions are highly unstable for initial amplitudes larger than one. (KR).