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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Convergence of Finite Difference Schemes for a Multidimensional Boussinesq Equation
verfasst von : Natalia T. Kolkovska
Erschienen in: Numerical Methods and Applications
Verlag: Springer Berlin Heidelberg
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Conservative finite difference schemes
for the numerical solution of multi-dimensional Boussinesq-type equations are constructed and studied theoretically. Depending on the way the nonlinear term
f
(
u
) is approximated, two families of finite difference schemes are developed. Error estimates for these numerical methods in the uniform metric and the Sobolev space
$W_2^1$
are obtained. The extensive numerical experiments given in [7] for the one-dimensional problem show good precision and full agreement between the theoretical results and practical evaluation for single soliton and the interaction between two solitons.