Abstract
We construct and analyze a multicomponent alternating direction method (a vector additive scheme) for the numerical solution of the multidimensional Boussinesq Paradigm Equation (BPE). In contrast to the standard splitting methods at every time level a system of many finite difference schemes is solved. Thus, a vector of the discrete solutions to these schemes is found. It is proved that these discrete solutions converge to the continuous solution in the uniform mesh norm with O(|h|2 + τ) order. The method provides full approximation to BPE and is efficient in implementation. The numerical rate of convergence and the altitudes of the crests of the traveling waves are evaluated.
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Kolkovska, N., Angelow, K. (2013). A Multicomponent Alternating Direction Method for Numerical Solution of Boussinesq Paradigm Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_41
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DOI: https://doi.org/10.1007/978-3-642-41515-9_41
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